Question

Solve the equation (x - 5)² = 100 A) {15} B) {-5, 5)C) {-5, 15}D) {-15, 5}

Answer 1

We want to solve

`(x-5)^(2)=100`

This becomes

`\begin{gathered} (x-5)^(2)=100 \\ \text{squaroot both sides } \\ \sqrt[]{(x-5)^(2)}=\sqrt[]{100} \\ \text{Square cancels square root} \\ x-5=\sqrt[]{100} \\ i\text{ntroduce }\pm\text{ to the square root } \\ x-5=\pm\text{ }\sqrt[]{100} \\ \end{gathered}`

So, we have

`\begin{gathered} x-5=\pm\text{ }\sqrt[]{100} \\ x-5=\pm10 \\ x=5\pm10 \\ \text{either } \\ x=5+10=15 \\ Or \\ x=5-10=-5 \\ x=(-5,15) \end{gathered}`

Option C is correct