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This calculator is a quadratic solver that solves a quadratic polynomial equation of the form ax2 + bx + c = 0 with respect to x, where a is 0, using the sum of squares method. The calculator solution will show you the work of solving a quadratic equation by completing the square to solve the entered equation for real and complex roots. Completing the square when a is not equal to 1 To complete the square when a is greater than 1 or less than 1 but not equal to 0, subtract a from all other conditions. For example, find the solution by completing the square: (a e 1, a = 2), so divide by 2 (dfrac 22x^2 - dfrac 122x+ dfrac 7 2 = dfrac 02), which gives (x^2 - 6x + dfrac 72 = 0) Now continue solving this quadratic equation by completing the quadratic method. Squaring for b = 0 If you dont have an x term because b is 0, you will have an easier time solving the equation and only need to solve for the square of the term. For example: Solution by completing the square: Remove the term b by 0 to get: Leave the (x ) terms to the left and move the constant to the right, adding it to both sides So, take the square root of both sides. already know that there are several ways to solve quadratic equations. Have you tried to complete the square yet? Lets try it now! What does it mean to fill a square? Squaring is a method of adding and subtracting the same value from an expression to write it as a perfect square. Remember: A quadratic equation is an equation in which the variable is raised to the second power. We should also recall the standard form of a quadratic equation, which looks like this: Defining a quadratic equation is another tool in your toolbox for solving a quadratic equation. Youll find that even outside of quadratics, you can work much more efficiently when you start to understand which method to use and when. Take it as a fun challenge – see how easily you can do it! How to fill a square Lets count and find out how to fill a square! The best way to learn something is to see it in action, so well discuss some examples together. Solve this quadratic equation by completing the square: Move the constant to the right side of the equation and change its sign: $$ x ^ 2 + 4x = - 1 $$ same value (remember addition and subtraction!): $$ x ^ 2 + 4x + mathord ? = -1 + mathord ? $$ Write the expression as a product of the factors $$ 2 $$ and $$ x $$ so that our expression has the same structure as the formula we want to use: $$ x ^ 2 + 2 imes x imes2 + mathord ? = -1 + mathord ? $$ Since $$ 2 $$ is an intermediate component, add $$ 2 ^ 2 $$ to both sides of the equation: $$ x ^ 2 + 2^2 ims 2 + 2^2 = -1 + 2^2$$ Remember the sum formula square $$a^2 + 2a b + b ^ 2 = (a + b) ^ 2 $ $?This calculator is a quadratic equation solver that solves a quadratic polynomial equation of the form ax2 + bx + c = 0 x where a is 0 using the square completion method. Solver Calculator shows you the work of solving a quadratic equation by completing the square to solve the given equation for real and complex roots. Completing a square when a is not equal to 1 To complete a square when a is greater than 1 or less than 1 but not equal to 0, subtract the value of a from all other terms. For example, find the solution by completing the square: ( a e 1, a = 2 ) so divide by 2 ( dfrac22x^2 - dfrac122x + dfrac 7 2 = dfrac02 ), which gives us ( x^2 - 6x + dfrac72 = 0 ) We now proceed to solve this quadratic equation with the square completion method. Completing the Square for b = 0 If you dont have an x term because b is 0, it will be easier for you to solve the equation and you will only have to solve the square. For example: Solving by completing the square: Remove the b term by 0 and you get: Leave the ( x ) terms on the left and shift the constant to the right and add it to both sides. So take the square root of both sides. You already know that there are several ways to solve quadratic equations. Have you tried filling the square yet? Lets try it now! What does it mean to fill a square? The square is a method of adding and subtracting the same value from an expression to write it as a perfect square. Remember: a quadratic equation is an equation in which the variable is squared. Well also need a reminder of the standard form of a quadratic equation, which looks like this: Completing the square is another tool in your toolbox for solving quadratic equations. Youll find that you can work much more efficiently outside of quadratic calculations if you start to understand which method to use and when. Take it as a fun challenge - see how easy you can make things! How to Complete a Square Lets dive into the math and find out how to complete a square! The best way to learn something is to see it in action, so lets look at some examples together. Solve this quadratic equation by completing the square: Move the constant to the right side of the equation and change its sign: $$x^2+4x=-1$$ To complete the square while keeping the ratio between the sides of the equation, add one to both sides and to the same value (remember that the property of addition and subtraction is the same!): $$x^2+4x+mathord? =-1+mathord ? $$ Write the expression as the product of the factors $$2$$ and $$x$$ so that our expression has the same structure as the formula we want to use: $$x^2+2 imes x imes2 + mathord ? =-1+mathord?$$ Since $$2$$ is part of the middle term, add $$2^2$$ to both sides of the equation: $$x^2 +2 imes x imes 2+2^2 =-1+2^2$$ Remember the square sum formula $$a^2+2ab + b^2=( a+b)^2$$?
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