Question

What are the solutions of the quadratic equation?

x^2 + 7x = -12
(a) x = -2 and x = -5
(b) x = 2 and x = -5
(c) x = 2 and x = 5
(d) x = -2 and x = 5

Answer 1

The solutions to the quadratic equation x^2 + 7x = -12 are found by rearranging the equation into the form ax^2+bx+c=0 and then using the quadratic formula. The quadratic formula yields x = -3 and x = -4, which means none of the options provided in the question are correct.

Step-by-step explanation:

To solve the quadratic equation x2 + 7x = -12, we first need to rearrange it into the standard form ax2+bx+c = 0. By adding 12 to both sides of the equation, we get x2 + 7x + 12 = 0. Now we can solve the equation using the quadratic formula.

The quadratic formula is:
x = −b ± √(b2 - 4ac) /
(2a)

For our equation, a = 1, b = 7, and c = 12. Plugging these values into the formula:

• x = −7 ± √(72 − 4∗1∗12) / (2∗1)
• x = −7 ± √(49 − 48) / 2
• x = −7 ± √(1) / 2
• x = −7 ± 1 / 2

The two solutions are:

• x = (−7 + 1) / 2 = −3
• x = (−7 − 1) / 2 = −4

Therefore, the solutions to the equation x2 + 7x = -12 are x = -3 and x = -4. Thus, options (a), (b), (c), and (d) provided in the question are all incorrect.