4u^2+4u+7=75

Solution for 4u^2+4u+7=75 equation:

Simplifying
4u2 + 4u + 7 = 75

Reorder the terms:
7 + 4u + 4u2 = 75

Solving
7 + 4u + 4u2 = 75

Solving for variable 'u'.

Reorder the terms:
7 + -75 + 4u + 4u2 = 75 + -75

Combine like terms: 7 + -75 = -68
-68 + 4u + 4u2 = 75 + -75

Combine like terms: 75 + -75 = 0
-68 + 4u + 4u2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-17 + u + u2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-17 + u + u2)' equal to zero and attempt to solve:

Simplifying
-17 + u + u2 = 0

Solving
-17 + u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + u + 17 + u2 = 0 + 17

Reorder the terms:
-17 + 17 + u + u2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + u + u2 = 0 + 17
u + u2 = 0 + 17

Combine like terms: 0 + 17 = 17
u + u2 = 17

The u term is u.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
u + 0.25 + u2 = 17 + 0.25

Reorder the terms:
0.25 + u + u2 = 17 + 0.25

Combine like terms: 17 + 0.25 = 17.25
0.25 + u + u2 = 17.25

Factor a perfect square on the left side:
(u + 0.5)(u + 0.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(u + 0.5) equal to 4.153311931 and -4.153311931.

Subproblem 1
u + 0.5 = 4.153311931

Simplifying
u + 0.5 = 4.153311931

Reorder the terms:
0.5 + u = 4.153311931

Solving
0.5 + u = 4.153311931

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = 4.153311931 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = 4.153311931 + -0.5
u = 4.153311931 + -0.5

Combine like terms: 4.153311931 + -0.5 = 3.653311931
u = 3.653311931

Simplifying
u = 3.653311931

Subproblem 2
u + 0.5 = -4.153311931

Simplifying
u + 0.5 = -4.153311931

Reorder the terms:
0.5 + u = -4.153311931

Solving
0.5 + u = -4.153311931

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = -4.153311931 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = -4.153311931 + -0.5
u = -4.153311931 + -0.5

Combine like terms: -4.153311931 + -0.5 = -4.653311931
u = -4.653311931

Simplifying
u = -4.653311931

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.653311931, -4.653311931}
Solution
u = {3.653311931, -4.653311931}