To solve the quadratic equation (x+6)^2=8 using square roots, we need to isolate x first.
Taking the square root of both sides gives:
√((x+6)^2) = √8
Simplifying the left side:
|x+6| = √8
We can now solve for x by considering both positive and negative square roots.
Case 1: √8 = √(4*2) = √4 * √2 = 2√2
|x+6| = 2√2
For positive square root:
x + 6 = 2√2
x = -6 + 2√2 ≈ -1.17
For negative square root:
x + 6 = -2√2
x = -6 - 2√2 ≈ -6.83
Case 2: √8 = -2√2 (ignoring since absolute value cannot be negative)
Therefore, the solutions to the quadratic equation (x+6)^2 = 8 using square roots are approximately -1.17 and -6.83.
Solve the following quadratic equation using square roots: (x+6)22=8 .(1 point) Responses {−1.17,−6.83} left brace negative 1.17 comma negative 6.83 right brace {−2,−10} left brace negative 2 comma negative 10 right brace {10,−22} left brace 10 comma negative 22 right brace {−0.34,−11.66}
1 answer