To solve the quadratic equation using square roots, we can start by taking the square root of both sides of the equation:
√((x−18)²) = √196
Simplifying further, we have:
|x−18| = √196
Taking the square root of 196 gives us 14:
|x−18| = 14
Now we can set up two equations:
1. x−18 = 14
2. x−18 = -14
For the first equation, we solve for x by adding 18 to both sides:
x−18+18 = 14+18
x = 32
For the second equation, we solve for x by adding 18 to both sides:
x−18+18 = -14+18
x = 4
Therefore, the solutions to the quadratic equation are {32, 4}.
Solve the following quadratic equation using square roots: (x−18)2=196 .(1 point) Responses {21,5} left brace 21 comma 5 right brace {32,4} left brace 32 comma 4 right brace {214,−178} left brace 214 comma negative 178 right brace {−4,−32}
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