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Simplifying -13w2 + 38w + -15 = 0 Reorder the terms: -15 + 38w + -13w2 = 0 Solving -15 + 38w + -13w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. 1.153846154 + -2.923076923w + w2 = 0 Move the constant term to the right: Add '-1.153846154' to each side of the equation. 1.153846154 + -2.923076923w + -1.153846154 + w2 = 0 + -1.153846154 Reorder the terms: 1.153846154 + -1.153846154 + -2.923076923w + w2 = 0 + -1.153846154 Combine like terms: 1.153846154 + -1.153846154 = 0.000000000 0.000000000 + -2.923076923w + w2 = 0 + -1.153846154 -2.923076923w + w2 = 0 + -1.153846154 Combine like terms: 0 + -1.153846154 = -1.153846154 -2.923076923w + w2 = -1.153846154 The w term is -2.923076923w. Take half its coefficient (-1.461538462). Square it (2.136094676) and add it to both sides. Add '2.136094676' to each side of the equation. -2.923076923w + 2.136094676 + w2 = -1.153846154 + 2.136094676 Reorder the terms: 2.136094676 + -2.923076923w + w2 = -1.153846154 + 2.136094676 Combine like terms: -1.153846154 + 2.136094676 = 0.982248522 2.136094676 + -2.923076923w + w2 = 0.982248522 Factor a perfect square on the left side: (w + -1.461538462)(w + -1.461538462) = 0.982248522 Calculate the square root of the right side: 0.991084518 Break this problem into two subproblems by setting (w + -1.461538462) equal to 0.991084518 and -0.991084518.Subproblem 1
w + -1.461538462 = 0.991084518 Simplifying w + -1.461538462 = 0.991084518 Reorder the terms: -1.461538462 + w = 0.991084518 Solving -1.461538462 + w = 0.991084518 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.461538462' to each side of the equation. -1.461538462 + 1.461538462 + w = 0.991084518 + 1.461538462 Combine like terms: -1.461538462 + 1.461538462 = 0.000000000 0.000000000 + w = 0.991084518 + 1.461538462 w = 0.991084518 + 1.461538462 Combine like terms: 0.991084518 + 1.461538462 = 2.45262298 w = 2.45262298 Simplifying w = 2.45262298Subproblem 2
w + -1.461538462 = -0.991084518 Simplifying w + -1.461538462 = -0.991084518 Reorder the terms: -1.461538462 + w = -0.991084518 Solving -1.461538462 + w = -0.991084518 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.461538462' to each side of the equation. -1.461538462 + 1.461538462 + w = -0.991084518 + 1.461538462 Combine like terms: -1.461538462 + 1.461538462 = 0.000000000 0.000000000 + w = -0.991084518 + 1.461538462 w = -0.991084518 + 1.461538462 Combine like terms: -0.991084518 + 1.461538462 = 0.470453944 w = 0.470453944 Simplifying w = 0.470453944Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.45262298, 0.470453944}
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