# GRE Algebra | Solving Quadratic Equations

In algebra, a quadratic equation can be written in the form:

ax2 + bx + c = 0

where x is the variable and a, b, c are the real numbers and a≠0. If a=0 then it will be a linear equation not quadratic because no second order term.

If quadratic equation has solution then it can be found by using the quadratic formula. • Example-1: Solve the quadratic equation for x,
x2 + 10x -24 = 0

Solution: In the quadratic equation, we have,

a=1, b=10 and c=-24   Hence, two solutions for the above equations are:

x = 4/2 = 2,
And
x = -24/2 = -12 
• Example-2: Solve the quadratic equation using factorization,
x2 + 2x - 15 = 0

Solution: Given equation,

x2 + 2x - 15 = 0

It can be factorize as,

x2 -3x + 5x - 15 = 0
x(x - 3) + 5(x - 3) = 0
(x - 3)(x + 5) = 0 

Hence, two solutions for x are:

x = 3 and x = -5
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