Final answer:
To solve the equation -12 = -96x², divide by -96 and take the square root of both sides, resulting in two solutions: x = 0.3536 or x = -0.3536.
Step-by-step explanation:
The equation we need to solve is -12 = -96x². To solve for x, we begin by dividing both sides of the equation by -96, which simplifies the equation to x² = 12/96. This further reduces to x² = 1/8. Now, to find the value of x, we take the square root of both sides of the equation. This yields two solutions since a square root can be both positive and negative. Therefore, x = √(1/8) or x = -√(1/8). Simplifying the square root of 1/8, we get x = 1/√8 or x = -1/√8. To express this in decimal form, the approximate solutions are x = 0.3536 or x = -0.3536.