(4w-1)w=88

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Solution for (4w-1)w=88 equation:


Simplifying
(4w + -1) * w = 88

Reorder the terms:
(-1 + 4w) * w = 88

Reorder the terms for easier multiplication:
w(-1 + 4w) = 88
(-1 * w + 4w * w) = 88
(-1w + 4w2) = 88

Solving
-1w + 4w2 = 88

Solving for variable 'w'.

Reorder the terms:
-88 + -1w + 4w2 = 88 + -88

Combine like terms: 88 + -88 = 0
-88 + -1w + 4w2 = 0

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

Divide each side by '4'.
-22 + -0.25w + w2 = 0

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -0.25w + 22 + w2 = 0 + 22

Reorder the terms:
-22 + 22 + -0.25w + w2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -0.25w + w2 = 0 + 22
-0.25w + w2 = 0 + 22

Combine like terms: 0 + 22 = 22
-0.25w + w2 = 22

The w term is -0.25w.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25w + 0.015625 + w2 = 22 + 0.015625

Reorder the terms:
0.015625 + -0.25w + w2 = 22 + 0.015625

Combine like terms: 22 + 0.015625 = 22.015625
0.015625 + -0.25w + w2 = 22.015625

Factor a perfect square on the left side:
(w + -0.125)(w + -0.125) = 22.015625

Calculate the square root of the right side: 4.692081095

Break this problem into two subproblems by setting 
(w + -0.125) equal to 4.692081095 and -4.692081095.

Subproblem 1

w + -0.125 = 4.692081095 Simplifying w + -0.125 = 4.692081095 Reorder the terms: -0.125 + w = 4.692081095 Solving -0.125 + w = 4.692081095 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + w = 4.692081095 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + w = 4.692081095 + 0.125 w = 4.692081095 + 0.125 Combine like terms: 4.692081095 + 0.125 = 4.817081095 w = 4.817081095 Simplifying w = 4.817081095

Subproblem 2

w + -0.125 = -4.692081095 Simplifying w + -0.125 = -4.692081095 Reorder the terms: -0.125 + w = -4.692081095 Solving -0.125 + w = -4.692081095 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + w = -4.692081095 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + w = -4.692081095 + 0.125 w = -4.692081095 + 0.125 Combine like terms: -4.692081095 + 0.125 = -4.567081095 w = -4.567081095 Simplifying w = -4.567081095

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.817081095, -4.567081095}

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