Question

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$x^{2}-7=57$$

Short answer

The solution to the equation \(x^{2}-7=57\) is \(x = \pm 8\)

Step-by-step solution

Reorganize the equation

The first step involves reorganizing the equation to get the unknown variable, x on one side of the equation. This can be done by adding 7 to both sides of the equation. This will result in the equation: \(x^{2} = 57+7\)

Simplify the equation

Combine like terms on the right side of the equation to simplify it which gives: \(x^{2} = 64\)

Solve for x

Now, to get the value of x, take the square root of both sides of the equation. But, don't forget that when you take the square root you always get 2 values, one negative and one positive. So, it results in \(x = \pm \sqrt{64}\)

Final Answer

Since \(\sqrt{64}\) equals 8, the final solution is \(x = \pm 8\)