Solve the equation by completing the square. Round to the nearest tenth.
x squared plus 8 x equals 10
(1 point)
Responses
1.1, 9.1
1.1, 9.1
1.1, negative 9.1
1.1, Image with alt text: negative 9.1
negative 1 point 1, 9.1
Image with alt text: negative 1 point 1 , 9.1
negative 1 point 1 comma negative 9 point 1
Step 1: Move the constant to the other side:
x^2 + 8x = 10
x^2 + 8x - 10 = 0
Step 2: To complete the square, take half of the coefficient of x (which is 8) and square it:
(8/2)^2 = 16
Step 3: Add and subtract the value from step 2 to both sides of the equation:
x^2 + 8x + 16 = 10 + 16
x^2 + 8x + 16 = 26
Step 4: Factor the left side and simplify the right side:
(x + 4)^2 = 26
Step 5: Solve for x by taking the square root of both sides:
x + 4 = ±√26
x = -4 ± √26
Rounded to the nearest tenth:
x ≈ -4 + 5.1 ≈ 1.1
x ≈ -4 - 5.1 ≈ -9.1
Therefore, the solutions are approximately 1.1 and -9.1.