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Simplifying 4w2 + -15w + -9 = 0 Reorder the terms: -9 + -15w + 4w2 = 0 Solving -9 + -15w + 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'. -2.25 + -3.75w + w2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -3.75w + 2.25 + w2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -3.75w + w2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -3.75w + w2 = 0 + 2.25 -3.75w + w2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -3.75w + w2 = 2.25 The w term is -3.75w. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75w + 3.515625 + w2 = 2.25 + 3.515625 Reorder the terms: 3.515625 + -3.75w + w2 = 2.25 + 3.515625 Combine like terms: 2.25 + 3.515625 = 5.765625 3.515625 + -3.75w + w2 = 5.765625 Factor a perfect square on the left side: (w + -1.875)(w + -1.875) = 5.765625 Calculate the square root of the right side: 2.401171589 Break this problem into two subproblems by setting (w + -1.875) equal to 2.401171589 and -2.401171589.Subproblem 1
w + -1.875 = 2.401171589 Simplifying w + -1.875 = 2.401171589 Reorder the terms: -1.875 + w = 2.401171589 Solving -1.875 + w = 2.401171589 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + w = 2.401171589 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + w = 2.401171589 + 1.875 w = 2.401171589 + 1.875 Combine like terms: 2.401171589 + 1.875 = 4.276171589 w = 4.276171589 Simplifying w = 4.276171589Subproblem 2
w + -1.875 = -2.401171589 Simplifying w + -1.875 = -2.401171589 Reorder the terms: -1.875 + w = -2.401171589 Solving -1.875 + w = -2.401171589 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + w = -2.401171589 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + w = -2.401171589 + 1.875 w = -2.401171589 + 1.875 Combine like terms: -2.401171589 + 1.875 = -0.526171589 w = -0.526171589 Simplifying w = -0.526171589Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.276171589, -0.526171589}
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