Question

Solve quadratic equation$y^2+12y+36=32$using a square root property.

Short answer

The values of $y$are$-6-4\sqrt{2}$and$-6+4\sqrt{2}$

Step-by-step solution

Step 1. Write the given information

Consider the quadratic equation $y^2+12y+36=32$

Step 2. Factor the perfect square trinomial

${\left(y+6\right)}^2=32$

Step 3. Use square root property

$y+6=\pm \sqrt{32}$

$\Rightarrow y=-6\pm 4\sqrt{2}$

$\Rightarrow y=-6-4\sqrt{2}$and$y=-6+4\sqrt{2}$