Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+27)^2−6=−3 .(1 point) {}
To solve the equation (x+27)^2 - 6 = -3, we will start by isolating the squared term on one side of the equation.
(x+27)^2 - 6 = -3
(x+27)^2 = -3 + 6
(x+27)^2 = 3
Next, we will take the square root of both sides of the equation to eliminate the squared term.
√[(x+27)^2] = √3
x+27 = ±√3
Now, we will solve for x by subtracting 27 from both sides of the equation.
x+27-27 = ±√3-27
x = -27±√3
Rounding to the nearest hundredth, we get:
x ≈ -27.00 ± √3