Solve the following quadratic equation using square roots: -9+(x-3)^2/-4 =- 4.
• {28,-22}
• {8,-2}
• {2,-8}
• {16,-10}
To solve the quadratic equation, we'll start by simplifying the left side of the equation:
-9 + (x-3)^2 = -4
Now, let's get rid of the constant term on the left side by adding 9 to both sides of the equation:
(x-3)^2 = -4 + 9
(x-3)^2 = 5
Next, we'll take the square root of both sides of the equation:
√((x-3)^2) = ±√5
|x-3| = ±√5
Now, we'll consider two cases:
Case 1: |x-3| = √5
In this case, x-3 can be either √5 or -√5, so we have two possible solutions:
x-3 = √5 --> x = 3 + √5 --> x = 3 + √5 ≈ 5.24
x-3 = -√5 --> x = 3 - √5 --> x = 3 - √5 ≈ 0.76
Case 2: |x-3| = -√5
In this case, |-√5| is not possible, so there are no solutions in this case.
Therefore, the solutions to the quadratic equation are:
{x = 3 + √5, x = 3 - √5} or approximately {x ≈ 5.24, x ≈ 0.76}
None of the given answer choices match these solutions.