Question

Solve the equation. $$x^{2}+25=81$$

Short answer

The solutions to the equation \(x^{2}+25=81\) are \(x = 2\sqrt{14}\) and \(x = -2\sqrt{14}\).

Step-by-step solution

Isolate the x Square Term

First, isolate the \(x^2\) on one side of the equation. To do this, subtract 25 from both sides of the equation to get: \(x^{2} + 25 - 25 = 81 - 25\), which simplifies to \(x^{2} = 56\).

Square Root both Sides

Next, find the value for \(x\), perform a square root on both sides of the equation as \(x\) is squared in the equation. However, remember when you apply square root on an equation, you get both positive and negative solutions. Therefore, \(x = \pm \sqrt{56}\).

Simplify the Square Root

The square root of 56 does not give a whole number. We can simplify it to \(x = \pm 2\sqrt{14}\).