Q 31. - Intermediate Algebra

Question

Solve quadratic equation ${\left(a-7\right)}^2+5=55$ using square root property

Step-by-Step Solution

Answer

The values of $a$ are $7+5\sqrt{2}$ and $7-5\sqrt{2}$

Step 1. Given information

The quadratic equation ${\left(a-7\right)}^2+5=55$

$\Rightarrow {\left(a-7\right)}^2=50$

Step 2. Use square root property

$\Rightarrow a-7=\pm \sqrt{50}$

$\Rightarrow a-7=\pm 5\sqrt{2}$

$\Rightarrow a=7\pm 5\sqrt{2}$

$\Rightarrow a=7+5\sqrt{2}$ and $a=7-5\sqrt{2}$