To complete the square when a is greater than 1 or less than 1 but not equal to 0, divide both sides of the equation by a. Remember you will have 2 solutions, a positive solution and a negative solution, because you took the square root of the right side of the equation.Ĭompleting the Square when a is Not Equal to 1 Solving quadratic equations: There are a number of different methods for solving a quadratic equation, such as computing the square root, factoring, completing. Isolate x on the left by subtracting or adding the numeric constant on both sides.Rewrite the perfect square on the left to the form (x + y) 2.

Add this result to both sides of the equation.

Take the b term, divide it by 2, and then square it.

Move the c term to the right side of the equation by subtracting it from or adding it to both sides of the equation.

Your b and c terms may be fractions after this step.

If a ≠ 1, divide both sides of your equation by a.

Then, solve the equation by finding the value of the variable that makes the equation true. The calculator below solves the quadratic equation of ax 2 + bx + c 0. Determine the sign of the expression in that interval. Use the roots to divide the number line into intervals.

• First, arrange your equation to the form ax 2 + bx + c = 0 How do you solve algebraic expressions To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. How do you solve quadratic inequalities To solve a quadratic inequality write the inequality in the standard form ax2 + bx + c < 0 or ax2 + bx + c > 0, find the roots of the quadratic equation.

It takes a few steps to complete the square of a quadratic equation. If it is not 1, divide both sides of the equation by the a term and then continue to complete the square as explained below. You can use the complete the square method when it is not possible to solve the equation by factoring.įirst, make sure that the a term is 1.

What is Completing the Square?Ĭompleting the square is a method of solving quadratic equations by changing the left side of the equation so that it is the square of a binomial. How do you find complex roots To find the complex roots of a quadratic equation use the formula: x (-bi (4ac b2))/2a. The solution shows the work required to solve a quadratic equation for real and complex roots by completing the square. What are complex roots Complex roots are the imaginary roots of a function.

Solving quadratic equations calculator