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Simplifying 10w2 + 36 + -38w2 + -27 + 15w = 0 Reorder the terms: 36 + -27 + 15w + 10w2 + -38w2 = 0 Combine like terms: 36 + -27 = 9 9 + 15w + 10w2 + -38w2 = 0 Combine like terms: 10w2 + -38w2 = -28w2 9 + 15w + -28w2 = 0 Solving 9 + 15w + -28w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -28 the coefficient of the squared term: Divide each side by '-28'. -0.3214285714 + -0.5357142857w + w2 = 0 Move the constant term to the right: Add '0.3214285714' to each side of the equation. -0.3214285714 + -0.5357142857w + 0.3214285714 + w2 = 0 + 0.3214285714 Reorder the terms: -0.3214285714 + 0.3214285714 + -0.5357142857w + w2 = 0 + 0.3214285714 Combine like terms: -0.3214285714 + 0.3214285714 = 0.0000000000 0.0000000000 + -0.5357142857w + w2 = 0 + 0.3214285714 -0.5357142857w + w2 = 0 + 0.3214285714 Combine like terms: 0 + 0.3214285714 = 0.3214285714 -0.5357142857w + w2 = 0.3214285714 The w term is -0.5357142857w. Take half its coefficient (-0.2678571429). Square it (0.07174744900) and add it to both sides. Add '0.07174744900' to each side of the equation. -0.5357142857w + 0.07174744900 + w2 = 0.3214285714 + 0.07174744900 Reorder the terms: 0.07174744900 + -0.5357142857w + w2 = 0.3214285714 + 0.07174744900 Combine like terms: 0.3214285714 + 0.07174744900 = 0.3931760204 0.07174744900 + -0.5357142857w + w2 = 0.3931760204 Factor a perfect square on the left side: (w + -0.2678571429)(w + -0.2678571429) = 0.3931760204 Calculate the square root of the right side: 0.627037495 Break this problem into two subproblems by setting (w + -0.2678571429) equal to 0.627037495 and -0.627037495.Subproblem 1
w + -0.2678571429 = 0.627037495 Simplifying w + -0.2678571429 = 0.627037495 Reorder the terms: -0.2678571429 + w = 0.627037495 Solving -0.2678571429 + w = 0.627037495 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.2678571429' to each side of the equation. -0.2678571429 + 0.2678571429 + w = 0.627037495 + 0.2678571429 Combine like terms: -0.2678571429 + 0.2678571429 = 0.0000000000 0.0000000000 + w = 0.627037495 + 0.2678571429 w = 0.627037495 + 0.2678571429 Combine like terms: 0.627037495 + 0.2678571429 = 0.8948946379 w = 0.8948946379 Simplifying w = 0.8948946379Subproblem 2
w + -0.2678571429 = -0.627037495 Simplifying w + -0.2678571429 = -0.627037495 Reorder the terms: -0.2678571429 + w = -0.627037495 Solving -0.2678571429 + w = -0.627037495 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.2678571429' to each side of the equation. -0.2678571429 + 0.2678571429 + w = -0.627037495 + 0.2678571429 Combine like terms: -0.2678571429 + 0.2678571429 = 0.0000000000 0.0000000000 + w = -0.627037495 + 0.2678571429 w = -0.627037495 + 0.2678571429 Combine like terms: -0.627037495 + 0.2678571429 = -0.3591803521 w = -0.3591803521 Simplifying w = -0.3591803521Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.8948946379, -0.3591803521}
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