Solve the equation by completing the square. Round to the nearest tenth.
x² + 8x = 10
(1 point)
a. 1.1, 9.1
b. 1.1, –9.1
c. –1.1, 9.1
d. –1.1, –9.1
To solve the equation by completing the square, we rearrange the equation to have only the quadratic term and linear term on one side:
x² + 8x = 10
Now, we can complete the square by adding the square of half the coefficient of the linear term (in this case, the coefficient is 8) to both sides of the equation:
x² + 8x + (8/2)² = 10 + (8/2)²
x² + 8x + 16 = 10 + 16
x² + 8x + 16 = 26
Next, we can simplify the equation:
(x + 4)² = 26
To solve for x, we take the square root of both sides, considering both the positive and negative square roots:
x + 4 = ±√26
Subtracting 4 from both sides:
x = -4 ± √26
Rounding to the nearest tenth:
x ≈ -1.1, 7.1
Therefore, the answer is:
d. –1.1, –9.1