Question

Solve for u.
(u-1)²=2u²+8u+25

Answer 1

u = -4 or -6

Explanation:

We know that,

( a + b ) = a² + 2ab + b²

Accordingly, let us solve the given equation.

( u - 1 )² = 2u² + 8u + 25

First, solve the brackets.

u² - 2u + 1 = 2u² + 8u + 25

Subtract u² by both sides.

-2u + 1 = 2u² - u² + 8u + 25

-2u + 1 = u² + 8u + 25

Now, add 2u by both sides.

1 = u² + 8u + 2u + 25

Subtract 1 by both sides.

0 = u² + 10u + 25 -1

0 = u² + 10u + 24

And solve the quadratic equation and solve for u.

0 = u² + 6u + 4u + 24

0 = u ( u + 6 ) + 4 ( u + 6 )

0 = ( u + 4 ) ( u + 6 )

Therefore,

u + 4 = 0

u = -4

or

u + 6 = 0

u = -6