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Simplifying w2 + -6w + -22 = -25w2 Reorder the terms: -22 + -6w + w2 = -25w2 Solving -22 + -6w + w2 = -25w2 Solving for variable 'w'. Combine like terms: w2 + 25w2 = 26w2 -22 + -6w + 26w2 = -25w2 + 25w2 Combine like terms: -25w2 + 25w2 = 0 -22 + -6w + 26w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + -3w + 13w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + -3w + 13w2)' equal to zero and attempt to solve: Simplifying -11 + -3w + 13w2 = 0 Solving -11 + -3w + 13w2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.8461538462 + -0.2307692308w + w2 = 0 Move the constant term to the right: Add '0.8461538462' to each side of the equation. -0.8461538462 + -0.2307692308w + 0.8461538462 + w2 = 0 + 0.8461538462 Reorder the terms: -0.8461538462 + 0.8461538462 + -0.2307692308w + w2 = 0 + 0.8461538462 Combine like terms: -0.8461538462 + 0.8461538462 = 0.0000000000 0.0000000000 + -0.2307692308w + w2 = 0 + 0.8461538462 -0.2307692308w + w2 = 0 + 0.8461538462 Combine like terms: 0 + 0.8461538462 = 0.8461538462 -0.2307692308w + w2 = 0.8461538462 The w term is -0.2307692308w. Take half its coefficient (-0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. -0.2307692308w + 0.01331360947 + w2 = 0.8461538462 + 0.01331360947 Reorder the terms: 0.01331360947 + -0.2307692308w + w2 = 0.8461538462 + 0.01331360947 Combine like terms: 0.8461538462 + 0.01331360947 = 0.85946745567 0.01331360947 + -0.2307692308w + w2 = 0.85946745567 Factor a perfect square on the left side: (w + -0.1153846154)(w + -0.1153846154) = 0.85946745567 Calculate the square root of the right side: 0.927074676 Break this problem into two subproblems by setting (w + -0.1153846154) equal to 0.927074676 and -0.927074676.Subproblem 1
w + -0.1153846154 = 0.927074676 Simplifying w + -0.1153846154 = 0.927074676 Reorder the terms: -0.1153846154 + w = 0.927074676 Solving -0.1153846154 + w = 0.927074676 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + w = 0.927074676 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + w = 0.927074676 + 0.1153846154 w = 0.927074676 + 0.1153846154 Combine like terms: 0.927074676 + 0.1153846154 = 1.0424592914 w = 1.0424592914 Simplifying w = 1.0424592914Subproblem 2
w + -0.1153846154 = -0.927074676 Simplifying w + -0.1153846154 = -0.927074676 Reorder the terms: -0.1153846154 + w = -0.927074676 Solving -0.1153846154 + w = -0.927074676 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + w = -0.927074676 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + w = -0.927074676 + 0.1153846154 w = -0.927074676 + 0.1153846154 Combine like terms: -0.927074676 + 0.1153846154 = -0.8116900606 w = -0.8116900606 Simplifying w = -0.8116900606Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.0424592914, -0.8116900606}Solution
w = {1.0424592914, -0.8116900606}
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