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Simplifying -4w2 + 20w + 3 = 0 Reorder the terms: 3 + 20w + -4w2 = 0 Solving 3 + 20w + -4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -5w + w2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -5w + 0.75 + w2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -5w + w2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -5w + w2 = 0 + 0.75 -5w + w2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -5w + w2 = 0.75 The w term is -5w. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5w + 6.25 + w2 = 0.75 + 6.25 Reorder the terms: 6.25 + -5w + w2 = 0.75 + 6.25 Combine like terms: 0.75 + 6.25 = 7 6.25 + -5w + w2 = 7 Factor a perfect square on the left side: (w + -2.5)(w + -2.5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (w + -2.5) equal to 2.645751311 and -2.645751311.Subproblem 1
w + -2.5 = 2.645751311 Simplifying w + -2.5 = 2.645751311 Reorder the terms: -2.5 + w = 2.645751311 Solving -2.5 + w = 2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + w = 2.645751311 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = 2.645751311 + 2.5 w = 2.645751311 + 2.5 Combine like terms: 2.645751311 + 2.5 = 5.145751311 w = 5.145751311 Simplifying w = 5.145751311Subproblem 2
w + -2.5 = -2.645751311 Simplifying w + -2.5 = -2.645751311 Reorder the terms: -2.5 + w = -2.645751311 Solving -2.5 + w = -2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + w = -2.645751311 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = -2.645751311 + 2.5 w = -2.645751311 + 2.5 Combine like terms: -2.645751311 + 2.5 = -0.145751311 w = -0.145751311 Simplifying w = -0.145751311Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.145751311, -0.145751311}
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