Final answer:
To solve ((x + 8)² - 7 = 0), rearrange it to x² + 16x + 57 = 0. Use the quadratic formula to find x = -10.65 and x = -5.35.
Step-by-step explanation:
To solve the equation ((x + 8)² - 7 = 0), we can rearrange it to x² + 16x + 57 = 0. Now, we can use the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values for a, b, and c from our equation, we get:
x = (-16 ± √(16² - 4(1)(57))) / (2(1))
Simplifying the expression under the square root, we have:
x = (-16 ± √(256 - 228)) / 2
x = (-16 ± √28) / 2
Now, we can simplify further:
x = (-16 ± 2√7) / 2
x = -8 ± √7
Since we need to round the solutions to two decimal places and list them from least to greatest, the solutions are approximately:
x ≈ -8 - 2.65
x ≈ -8 + 2.65
Therefore, the solutions to the equation are x ≈ -10.65 and x ≈ -5.35.