Question

Which equation is equivalent to the given equation? x^2+16x=22

Answer 1

Answer:answer is a (x+8)^2=86

Step-by-step explanation:

x+8=±√

​86

​

​​

2 Break down the problem into these 2 equations.

x+8=\sqrt{86}x+8=√

​86

​

​​

x+8=-\sqrt{86}x+8=−√

​86

​

​​

3 Solve the 1st equation: x+8=\sqrt{86}x+8=√

​86

​

​​ .

x=\sqrt{86}-8x=√

​86

​

​​ −8

4 Solve the 2nd equation: x+8=-\sqrt{86}x+8=−√

​86

​

​​ .

x=-\sqrt{86}-8x=−√

​86

​

​​ −8

5 Collect all solutions.

x=\sqrt{86}-8,-\sqrt{86}-8x=√

​86

​

​​ −8,−√

​86

​

​​ −8

x

​2

​​ +16x−22=0

2 Use the Quadratic Formula.

x=\frac{-16+2\sqrt{86}}{2},\frac{-16-2\sqrt{86}}{2}x=

​2

​

​−16+2√

​86

​

​​

​​ ,

​2

​

​−16−2√

​86

​

​​

​​

3 Simplify solutions.

x=-8+\sqrt{86},-8-\sqrt{86}x=−8+√

​86

​

​​ ,−8−√

​86

​

​​