when a number,x, is added to its square, the answer is 72

Question

write an equation in x and solve it to find two numbers. verify that both numbers satisfy the equation.

Answer 1

x + x² = 72

x² + x - 72 = 0

(x + 9)(x - 8) = 0

For the left side to equal 0, either x + 9 or x - 8 has to equal 0.

x + 9 = 0

x = -9

(-9)² + (-9) = 72

81 - 9 = 72

72 = 72

Boom.

x - 8 = 0

x = 8

8² + 8 = 72

64 + 8 = 72

72 = 72

Boom again.