3w^2-3w-588=0

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Solution for 3w^2-3w-588=0 equation:


Simplifying
3w2 + -3w + -588 = 0

Reorder the terms:
-588 + -3w + 3w2 = 0

Solving
-588 + -3w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-196 + -1w + w2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-196 + -1w + w2)' equal to zero and attempt to solve: Simplifying -196 + -1w + w2 = 0 Solving -196 + -1w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + -1w + 196 + w2 = 0 + 196 Reorder the terms: -196 + 196 + -1w + w2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + -1w + w2 = 0 + 196 -1w + w2 = 0 + 196 Combine like terms: 0 + 196 = 196 -1w + w2 = 196 The w term is -1w. 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. -1w + 0.25 + w2 = 196 + 0.25 Reorder the terms: 0.25 + -1w + w2 = 196 + 0.25 Combine like terms: 196 + 0.25 = 196.25 0.25 + -1w + w2 = 196.25 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = 196.25 Calculate the square root of the right side: 14.008925726 Break this problem into two subproblems by setting (w + -0.5) equal to 14.008925726 and -14.008925726.

Subproblem 1

w + -0.5 = 14.008925726 Simplifying w + -0.5 = 14.008925726 Reorder the terms: -0.5 + w = 14.008925726 Solving -0.5 + w = 14.008925726 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + w = 14.008925726 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = 14.008925726 + 0.5 w = 14.008925726 + 0.5 Combine like terms: 14.008925726 + 0.5 = 14.508925726 w = 14.508925726 Simplifying w = 14.508925726

Subproblem 2

w + -0.5 = -14.008925726 Simplifying w + -0.5 = -14.008925726 Reorder the terms: -0.5 + w = -14.008925726 Solving -0.5 + w = -14.008925726 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + w = -14.008925726 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = -14.008925726 + 0.5 w = -14.008925726 + 0.5 Combine like terms: -14.008925726 + 0.5 = -13.508925726 w = -13.508925726 Simplifying w = -13.508925726

Solution

The solution to the problem is based on the solutions from the subproblems. w = {14.508925726, -13.508925726}

Solution

w = {14.508925726, -13.508925726}

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