Answer:
x = 1
x = -2
Step-by-step explanation:
Hello!
We can solve the quadratic by factoring the equation.
Standard Form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]
Given our equation: [tex]x^2 + x - 2 = 0[/tex]
Find two numbers that multiply up to "ac" but add up to "b". The two numbers are 2 and -1. Expand x into 2x and -1x.
Factor by Grouping
- [tex]x^2 + x - 2 = 0[/tex]
- [tex]x^2 + 2x - x - 2 = 0[/tex]
- [tex]x(x + 2) -1(x + 2) = 0[/tex]
- [tex](x - 1)(x + 2) = 0[/tex]
Set each factor to 0 and solve for x:
- [tex]x - 1 = 0\\x = 1[/tex]
- [tex]x + 2 = 0\\x = -2[/tex]
The solutions for x are 1 and -2.
