Question

X^2+10x=9 to make it into a perfect square

Answer 1

Recall that

(a + b)² = a² + 2ab + b²

We want to add a constant to the left side to be able to form a squared binomial. If we let a = x, then

2ab = 10x = 2 • x • 5

so that b = 5, which tells us

(x + 5)² = x² + 10x + 25

So, we add 25 to both sides of the equation to get

x² + 10x + 25 = 9 + 25

and we simplify both sides to end up with

(x + 5)² = 34

If you want to go on to solve for x, we have

x + 5 = ± √34

x = -5 ± √34