Question

To solve by completing the square, what value should you add to each side of the equation.
x^2+16x=-4

Answer 1

\[(\frac{ b }{ 2 })^{2}\] use this. b in this equation is 16. that will give you the value.

Answer 2

Completing the square hinges on the algebraic property of raising a binomial to the power of \(2\). Observe:$$(a+b)^2=(a+b)(a+b)=a(a+b)+b(a+b)=a^2+ab+ab+b^2=a^2+2ab+b^2$$

In our case, we observe we have \(x^2+16x\) corresponding to \(a^2+2ab\), so \(x\) is our \(a\) and therefore \(b\) must be \(\frac12(16)=8\).

Notice all we're missing, then, is our final term \(b^2\). Since we deduced \(b=8\), we add \(b^2=64\) to our equation to yield:$$x^2+16x+64=-4+64=60\\(x+8)^2=6$$

Answer 3

So 8^2 = 64?

Answer 4

\(60\)*

Answer 5

so I would need to add 60 to each side of the equation?

Answer 6

Yes. that's it

Answer 7

16/2 = 8 8*8 = 64

Answer 8

@PECKE no you add \(64\), I was merely correcting my last line to \((x+8)^2=60\).

Answer 9

ahh okay, phew think I got it all Thanks