Question

For the quadratic equation f(x)=(x+6)²−49, what are the two solutions?

a. -13, 7
b. -1, 7
c. -13, -7
d. 1, -7

Answer 1

The solutions to the quadratic equation f(x) = (x+6)²−49 are x = 1 and x = -13.

Step-by-step explanation:

The quadratic equation is f(x) = (x+6)²−49. To find the solutions of this equation, we need to set it equal to zero and solve for x. So, we have (x+6)²−49 = 0. Expanding the square, we get x² + 12x + 36 - 49 = 0. Combining like terms and simplifying, we have x² + 12x - 13 = 0.

By using the quadratic formula, x = (-b ± √(b²-4ac))/2a, where a = 1, b = 12, and c = -13, we can find the solutions. Substituting the values, we get x = (-12 ± √(12²-4(1)(-13)))/2(1).

Simplifying further, we have x = (-12 ± √(144+52))/2, which becomes x = (-12 ± √(196))/2. Taking the square root, we have x = (-12 ± 14)/2. Finally, x = (-12 + 14)/2 = 1 and x = (-12 - 14)/2 = -13.