Question

(ALGEBRA ONE) 34 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

WHAT IS AN EQUIVALENT EQUATION THAT RESULTS FROM COMPLETING THE SQUARE

x^2+8x+19=0

Please show work to get points

Answer 1

`\large\boxed{x^2+8x+19=0\Rightarrow(x+4)^2=-3}`

Explanation:

`x^2+8x+19=0\qquad\text{subtract 19 from both sides}\\\\x^2+8x=-19\\\\x^2+2(x)(4)=-19\qquad\text{add}\ 4^2\ \text{to both sides}\\\\x^2+2(x)(4)+4^2=-19+4^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+4)^2=-3`