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 quadratic equation using square roots, we can isolate the variable on one side of the equation and then take the square root of both sides.
Given equation: (x+27)^2 - 6 = -3
First, we add 6 to both sides of the equation:
(x+27)^2 = 3
Next, we take the square root of both sides of the equation:
sqrt((x+27)^2) = sqrt(3)
Simplifying further:
|x+27| = sqrt(3)
The square root of 3 is approximately 1.73. Since we have an absolute value equation, we will consider both the positive and negative values.
For x + 27 = sqrt(3):
x = sqrt(3) - 27 ≈ -25.27
For x + 27 = -sqrt(3):
x = -sqrt(3) - 27 ≈ -28.73
The solutions to the quadratic equation (rounded to the nearest hundredth) are x ≈ -25.27 and x ≈ -28.73.