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Solve the quadratic equation below using square roots.

(x−4)2=25


(1 point)
Responses

{−29−−√, 29−−√}
{−29−−√, 29−−√}

{−2, 6}
{−2, 6}

{−3, 7}
{−3, 7}

{−1, 9}

1 answer

To solve the quadratic equation \((x−4)^2=25\) using square roots, we start by taking the square root of both sides:

\[ x - 4 = \pm 5 \]

This gives us two separate equations to solve:

  1. \(x - 4 = 5\)
  2. \(x - 4 = -5\)

Now, solving these equations:

For the first equation:

\[ x - 4 = 5 \] Adding 4 to both sides: \[ x = 5 + 4 = 9 \]

For the second equation:

\[ x - 4 = -5 \] Adding 4 to both sides: \[ x = -5 + 4 = -1 \]

So, the solutions are: \[ x = 9 \quad \text{and} \quad x = -1 \]

Thus, the answer is \({-1, 9}\).