Final answer:
To solve the equation -12x² = 34x - 28 using the AC method, rearrange it to form a quadratic equation set to 0. Then, apply the quadratic formula to find the solutions. The correct answer is (d) x = -7.
Step-by-step explanation:
The given equation is -12x² = 34x - 28. To solve this equation using the AC method, we need to rearrange it to form a quadratic equation set equal to 0. So, -12x² - 34x + 28 = 0. We can then use the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions are given by:
x = (-b ± √(b² - 4ac)) / (2a)
For our equation, a = -12, b = -34, and c = 28. Plugging these values into the formula, we can find the solutions:
x = (-(-34) ± √((-34)² - 4(-12)(28))) / (2(-12))
x = (34 ± √(1156 + 1344)) / -24
x = (34 ± √2500) / -24
x = (34 ± 50) / -24
So, the solutions are x = 2/3 and x = -7/2. Therefore, the correct answer is (d) x = -7.