Question

Solve for x in this equation
x² - x = 12

Answer 1

x = 4 x = -3

Explanation:

x² - x = 12

x² - x - 12 = 0

x² -1x - 12 = 0

find 2 numbers that when multiplied give you -12 and when added give you

they are -4 and 3

(x-4)(x+3)=0

(x-4) = 0

(x+3) = 0

x = 4

x = -3

Answer 2

Explanation:

the other solution is right, but that works only for very low, simple numbers, where you have limited options to play through.

there is a general way to solve any quadratic equation :

0 = ax² + bx + c

x = (-b ± sqrt(b² - 4ac))/(2a)

so, we have

x² - x - 12 = 0

a = 1

b = -1

c = -12

x = (1 ± sqrt((-1)² - 4×1×-12))/(2×1) =

= (1 ± sqrt(1 + 48))/2 = (1 ± sqrt(49))/2 =

= (1 ± 7)/2

x1 = (1 + 7)/2 = 8/2 = 4

x2 = (1 - 7)/2 = -6/2 = -3

so, the 2 solutions for the equation are

x = -3 and x = 4