Question

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

Answer 1

`(x+8)^2 = 86`

Explanation:

Given

`x^2 + 16x = 22`

Required

Determine an equivalent equation

`x^2 + 16x = 22`

Get the coefficient of x

`Coefficient = 16`

Divide this by 2

`Result = (16)/(2)`

`Result = 8`

Take its square

`Result = 8^2`

`Result = 64`

Add this to both sides of the equation

`x^2 + 16x + 64 = 22 + 64`

`x^2 + 16x + 64 = 86`

Expand the expression on the right hand side

`x^2 + 8x + 8x + 64 = 86`

Factorize

`x(x+8)+8(x+8) = 86`

`(x+8)(x+8) = 86`

`(x+8)^2 = 86`

Hence, the equivalent equation is
`(x+8)^2 = 86`