Question
solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+16)^2/9 = 7
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GPT 3.5
To solve the quadratic equation using square roots, we can start by isolating the squared term on one side of the equation.
First, multiply both sides of the equation by 9 to clear the fraction:
9 * (x+16)^2/9 = 7 * 9
(x+16)^2 = 63
Next, take the square root of both sides of the equation to eliminate the squared term:
√(x+16)^2 = √63
x+16 = ±√63
Now, let's solve for x:
x = -16 ± √63
Rounding to the nearest hundredth, x is approximately:
x ≈ -16 + √63 ≈ -16 + 7.94 ≈ -8.06
x ≈ -16 - √63 ≈ -16 - 7.94 ≈ -23.94
Therefore, the solutions to the quadratic equation are approximately x ≈ -8.06 and x ≈ -23.94.
First, multiply both sides of the equation by 9 to clear the fraction:
9 * (x+16)^2/9 = 7 * 9
(x+16)^2 = 63
Next, take the square root of both sides of the equation to eliminate the squared term:
√(x+16)^2 = √63
x+16 = ±√63
Now, let's solve for x:
x = -16 ± √63
Rounding to the nearest hundredth, x is approximately:
x ≈ -16 + √63 ≈ -16 + 7.94 ≈ -8.06
x ≈ -16 - √63 ≈ -16 - 7.94 ≈ -23.94
Therefore, the solutions to the quadratic equation are approximately x ≈ -8.06 and x ≈ -23.94.
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