Question

Solve the equation $y^2+8y=48$by completing the square and explain all your steps.

Short answer

The solution is$y=-12,y=4$

Step-by-step solution

Step 1. Given information

Equation:$y^2+8y=48$

Step 2. Calculation 

We have,

$y^2+8y=48$

$y^2+8y+{\left(\frac{1}{2}·\left(8\right)\right)}^2=48+{\left(\frac{1}{2}·\left(8\right)\right)}^2$ take half of 8 and square it, then add to both sides

$y^2+8y+16=48+16$

${\left(y+4\right)}^2=64$ factor the perfect square trinomial

$\sqrt{{\left(y+4\right)}^2}=\sqrt{64}$ using square root property

$y+4=\pm 8$ simplify

$y+4-4=-8-4,y+4-4=8-4$

$y=-12,y=4$