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Simplifying
(2u + 1)(2u + 1) + -2(2u + 1) + -15 = 0
Reorder the terms:
(1 + 2u)(2u + 1) + -2(2u + 1) + -15 = 0
Reorder the terms:
(1 + 2u)(1 + 2u) + -2(2u + 1) + -15 = 0
Multiply (1 + 2u) * (1 + 2u)
(1(1 + 2u) + 2u * (1 + 2u)) + -2(2u + 1) + -15 = 0
((1 * 1 + 2u * 1) + 2u * (1 + 2u)) + -2(2u + 1) + -15 = 0
((1 + 2u) + 2u * (1 + 2u)) + -2(2u + 1) + -15 = 0
(1 + 2u + (1 * 2u + 2u * 2u)) + -2(2u + 1) + -15 = 0
(1 + 2u + (2u + 4u2)) + -2(2u + 1) + -15 = 0
Combine like terms: 2u + 2u = 4u
(1 + 4u + 4u2) + -2(2u + 1) + -15 = 0
Reorder the terms:
1 + 4u + 4u2 + -2(1 + 2u) + -15 = 0
1 + 4u + 4u2 + (1 * -2 + 2u * -2) + -15 = 0
1 + 4u + 4u2 + (-2 + -4u) + -15 = 0
Reorder the terms:
1 + -2 + -15 + 4u + -4u + 4u2 = 0
Combine like terms: 1 + -2 = -1
-1 + -15 + 4u + -4u + 4u2 = 0
Combine like terms: -1 + -15 = -16
-16 + 4u + -4u + 4u2 = 0
Combine like terms: 4u + -4u = 0
-16 + 0 + 4u2 = 0
-16 + 4u2 = 0
Solving
-16 + 4u2 = 0
Solving for variable 'u'.
Move all terms containing u to the left, all other terms to the right.
Add '16' to each side of the equation.
-16 + 16 + 4u2 = 0 + 16
Combine like terms: -16 + 16 = 0
0 + 4u2 = 0 + 16
4u2 = 0 + 16
Combine like terms: 0 + 16 = 16
4u2 = 16
Divide each side by '4'.
u2 = 4
Simplifying
u2 = 4
Take the square root of each side:
u = {-2, 2}
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