Solve the following quadratic equation using square roots: (x−18)2=196.(1 point)%0D%0AResponses%0D%0A%0D%0A{32,4}%0D%0Aleft brace 32 comma 4 right brace%0D%0A%0D%0A%E2%80%8B {−4,−32}%0D%0A%E2%80%8B left brace negative 4 comma negative 32 right brace%0D%0A%0D%0A{214,−178}%0D%0Aleft brace 214 comma negative 178 right brace%0D%0A%0D%0A{21,5}
The given quadratic equation is:
(x − 18)² = 196
To solve for x using square roots, we take the square root of both sides of the equation. Remember that taking the square root of both sides introduces a plus or minus (±) sign:
√(x − 18)² = ±√196
Since the left side is the square root of a square, it simplifies to the absolute value of (x − 18), but since we have ± on the right side, this is automatically accounted for:
x − 18 = ±14
Now we have two separate equations to solve for x:
1. x − 18 = 14
2. x − 18 = -14
For the first equation:
x − 18 = 14
x = 14 + 18
x = 32
For the second equation:
x − 18 = -14
x = -14 + 18
x = 4
Thus, the two solutions are x = 32 and x = 4. These can be written as a set:
{32, 4}