Question

Use the quadratic formula to find both solutions to the quadratic equation given below. x^2 + 6x = 16.

A) x = 2, x = -8
B) x = 4, x = -10
C) x = 3, x = -9
D) x = 5, x = -7

Answer 1

The solutions to the quadratic equation x^2 + 6x = 16 using the quadratic formula are x = 2 and x = -8. These are found by first rearranging the equation to standard form and then applying the quadratic formula values a=1, b=6, and c=-16 to find the roots.

Step-by-step explanation:

To find the solutions to the quadratic equation x^2 + 6x = 16 using the quadratic formula, we first need to write the equation in the standard form ax^2 + bx + c = 0. Subtracting 16 from both sides of the given equation, we get x^2 + 6x - 16 = 0. Now, by identifying a=1, b=6, and c=-16, we can apply these values to the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values, we get:

x = (-6 ± √((6)^2 - 4(1)(-16))) / (2(1))

x = (-6 ± √(36 + 64)) / 2

x = (-6 ± √100) / 2

x = (-6 ± 10) / 2

Thus, we have two solutions:

1. x = (-6 + 10) / 2 = 4 / 2 = 2
2. x = (-6 - 10) / 2 = -16 / 2 = -8

So, the two solutions are x = 2 and x = -8, making the answer choice A) x = 2, x = -8, correct.