Question

Solve the equation algebraically. Check the solutions graphically. $$x^{2}-10=6$$

Short answer

The solutions to the equation are \(x = 4\) and \(x = -4\).

Step-by-step solution

Transform the equation

Start with the equation \(x^{2}-10=6\). To isolate \(x^{2}\) on one side, add 10 to both sides of the equation. This gives us the equation \(x^{2}=16\)

Isolate x

Isolate \(x\) by taking the square root of both sides. Note that \(x\) can be both positive and negative resulting in \(x = \pm 4\).

Check solutions graphically

Plot the original equation and the solutions. The graph should cross the x-axis at x = 4 and x = -4, confirming these as the solutions.