Question

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

Answer 1

Answer:

$(x+8)^2 = 86$

Step-by-step 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

$Result = \frac{16}{2}$

$Result = 8$

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 $(x+8)^2 = 86$