Answer:
[tex](x+8)^2 = 86[/tex]
Step-by-step explanation:
Given
[tex]x^2 + 16x = 22[/tex]
Required
Determine an equivalent equation
[tex]x^2 + 16x = 22[/tex]
Get the coefficient of x
[tex]Coefficient = 16[/tex]
Divide this by 2
[tex]Result = \frac{16}{2}[/tex]
[tex]Result = 8[/tex]
Take its square
[tex]Result = 8^2[/tex]
[tex]Result = 64[/tex]
Add this to both sides of the equation
[tex]x^2 + 16x + 64 = 22 + 64[/tex]
[tex]x^2 + 16x + 64 = 86[/tex]
Expand the expression on the right hand side
[tex]x^2 + 8x + 8x + 64 = 86[/tex]
Factorize
[tex]x(x+8)+8(x+8) = 86[/tex]
[tex](x+8)(x+8) = 86[/tex]
[tex](x+8)^2 = 86[/tex]
Hence, the equivalent equation is [tex](x+8)^2 = 86[/tex]
