u-16u^2-3=0

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Solution for u-16u^2-3=0 equation:


Simplifying
u + -16u2 + -3 = 0

Reorder the terms:
-3 + u + -16u2 = 0

Solving
-3 + u + -16u2 = 0

Solving for variable 'u'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.1875 + -0.0625u + u2 = 0

Move the constant term to the right:

Add '-0.1875' to each side of the equation.
0.1875 + -0.0625u + -0.1875 + u2 = 0 + -0.1875

Reorder the terms:
0.1875 + -0.1875 + -0.0625u + u2 = 0 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + -0.0625u + u2 = 0 + -0.1875
-0.0625u + u2 = 0 + -0.1875

Combine like terms: 0 + -0.1875 = -0.1875
-0.0625u + u2 = -0.1875

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.
-0.0625u + 0.25 + u2 = -0.1875 + 0.25

Reorder the terms:
0.25 + -0.0625u + u2 = -0.1875 + 0.25

Combine like terms: -0.1875 + 0.25 = 0.0625
0.25 + -0.0625u + u2 = 0.0625

Factor a perfect square on the left side:
(u + 0.5)(u + 0.5) = 0.0625

Calculate the square root of the right side: 0.25

Break this problem into two subproblems by setting 
(u + 0.5) equal to 0.25 and -0.25.

Subproblem 1

u + 0.5 = 0.25 Simplifying u + 0.5 = 0.25 Reorder the terms: 0.5 + u = 0.25 Solving 0.5 + u = 0.25 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 = 0.25 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = 0.25 + -0.5 u = 0.25 + -0.5 Combine like terms: 0.25 + -0.5 = -0.25 u = -0.25 Simplifying u = -0.25

Subproblem 2

u + 0.5 = -0.25 Simplifying u + 0.5 = -0.25 Reorder the terms: 0.5 + u = -0.25 Solving 0.5 + u = -0.25 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 = -0.25 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = -0.25 + -0.5 u = -0.25 + -0.5 Combine like terms: -0.25 + -0.5 = -0.75 u = -0.75 Simplifying u = -0.75

Solution

The solution to the problem is based on the solutions from the subproblems. u = {-0.25, -0.75}

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