what are the solutions to the equation x^2 - 2 = -3x

Answer 1

To solve the equation x^2 - 2 = -3x, we first need to set the equation equal to zero by moving all the terms to one side:

x^2 + 3x - 2 = 0

Next, we need to factor the quadratic equation. The factors of -2 that add up to 3 are 4 and -1:

(x + 4)(x - 1) = 0

Setting each factor equal to zero, we get:

x + 4 = 0 or x - 1 = 0

Solving for x in each equation:

x = -4 or x = 1

Therefore, the solutions to the equation x^2 - 2 = -3x are x = -4 and x = 1.