Solve h^2− 42 = −h using the quadratic formula. A. h = 0 or h = 7 B. h = −6 or h = 7 C. h = 6 or h = −7 D. h = −6 or h = −7

Hi there! The answer is C. h = 6 or h = −7

[tex] {h}^{2} - 42 = - h[/tex]
Add h to both sides of the equation.

[tex]h {}^{2} + h - 42 = 0[/tex]
First we need to find the discriminant (which can be found using the formula D = b^2 - 4ac)

[tex]d = 1 {}^{2} - 4 \times 1 \times - 42 \\ d = 1 + 168 \\ d = 169[/tex]

Now we can plug in our found values into the quadratic formula.

[tex]x = \frac{ - b - \sqrt{d} }{2a} \: \\ or \\ \: x = \frac{ - b + \sqrt{d} }{2a} [/tex]

Plug in.
[tex]x = \frac{ - 1 - \sqrt{196} }{2 \times 1} = \frac{ - 1 - 13}{2} = \frac{ - 14}{2} = - 7 \\ or \\ x = \frac{ - 1 + \sqrt{196} }{2 \times 1} = \frac{ - 1 + 13}{2} = \frac{ 12}{2} = 6[/tex]

Hence, the answer is C. h = 6 or h = −7