Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
x2 + 10 = –7x
A. x = 2, 5
B. x = –2, 5
C. x = 2, –5
D. x = –2, –5
Adding 7x to both sides, we get:
x^2 + 7x + 10 = 0
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
We have a = 1, b = 7, and c = 10. Substituting these values, we get:
x = (-7 ± √(7^2 - 4(1)(10))) / 2(1)
x = (-7 ± √9) / 2
x = (-7 ± 3) / 2
x = -5 or x = -2
Therefore, the answer is option B: x = -2, 5.
To solve the equation x^2 + 10 = -7x using the quadratic formula, we must first rewrite the equation in standard form (ax^2 + bx + c = 0):
x^2 + 7x + 10 = 0
Now we can identify the coefficients of the quadratic equation: a = 1, b = 7, and c = 10.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we have:
x = (-(7) ± √((7)^2 - 4(1)(10))) / (2(1))
Simplifying further:
x = (-7 ± √(49 - 40)) / 2
x = (-7 ± √9) / 2
x = (-7 ± 3) / 2
This gives us two possible solutions:
x1 = (-7 + 3) / 2 = -4 / 2 = -2
x2 = (-7 - 3) / 2 = -10 / 2 = -5
Therefore, the solutions to the equation x^2 + 10 = -7x are x = -2 and x = -5.
The correct answer is D. x = –2, –5.