Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+27)^2/−6=−3

Question

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Answer 1

To solve the quadratic equation using square roots, we first multiply both sides of the equation by -6:

(x+27)^2 = 18

Next, we take the square root of both sides of the equation:

√((x+27)^2) = ±√18

Simplifying the square root:

x + 27 = ±√18

Now, we isolate x by subtracting 27 from both sides of the equation:

x = -27 ± √18

Rounding to the nearest hundredth:

x ≈ -27 ± 4.24

Therefore, the solutions to the quadratic equation are approximately:

x ≈ -31.24 or -22.76