# The Steps to Solve Quadratic Equations

By Allison Horky
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The quadratic equation is most often used to solve curves on a graph when an object is experiencing projectile motion. The sides of the curve intersect the x-axis twice and y-axis once. The two answers the equation yields are the x-axis intersectioning points. The equation uses coefficients, a number multipied by a variable, and is equal to zero. Once you plug in your known values for the coefficients, you can solve for x.

## Set Up the Equation

Write the quadratic equation on a piece of paper. If you are solving for "x," the equation should read x = (-b ± √((b^2)-4ac)))/2a. The equation yields two answers for "x," corresponding to their location on the x-axis. The equation reads "x" equals the opposite of "b" plus or minus the square root of "b" squared minus 4 times "a" times "c" divided by 2 times "a." Also write the values you know about your curve; for example, if "a" equals 3, "b" equals 20 and "c" equals 10. Plug your known values into the quadratic equation. Using the example numbers given, you have x = (-5 ± √((20^2)-(4x3x10)))/(2x3).

## Solve the Equation

Solve the equation according to the order of operations to obtain a value for "x." Solve the value that is squared first and the numbers that are multiplied by each other second. The example now reads x = (-5 ± √(400-120))/6. Solve the subraction before solving for the square root phrases in the equation. The example now reads x = (-5 ± 16.73)/6.