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Simplifying 6w2 + -16w + -12 = 0 Reorder the terms: -12 + -16w + 6w2 = 0 Solving -12 + -16w + 6w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -8w + 3w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -8w + 3w2)' equal to zero and attempt to solve: Simplifying -6 + -8w + 3w2 = 0 Solving -6 + -8w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -2.666666667w + w2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.666666667w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + -2.666666667w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.666666667w + w2 = 0 + 2 -2.666666667w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.666666667w + w2 = 2 The w term is -2.666666667w. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667w + 1.777777780 + w2 = 2 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667w + w2 = 2 + 1.777777780 Combine like terms: 2 + 1.777777780 = 3.77777778 1.777777780 + -2.666666667w + w2 = 3.77777778 Factor a perfect square on the left side: (w + -1.333333334)(w + -1.333333334) = 3.77777778 Calculate the square root of the right side: 1.943650632 Break this problem into two subproblems by setting (w + -1.333333334) equal to 1.943650632 and -1.943650632.Subproblem 1
w + -1.333333334 = 1.943650632 Simplifying w + -1.333333334 = 1.943650632 Reorder the terms: -1.333333334 + w = 1.943650632 Solving -1.333333334 + w = 1.943650632 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + w = 1.943650632 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + w = 1.943650632 + 1.333333334 w = 1.943650632 + 1.333333334 Combine like terms: 1.943650632 + 1.333333334 = 3.276983966 w = 3.276983966 Simplifying w = 3.276983966Subproblem 2
w + -1.333333334 = -1.943650632 Simplifying w + -1.333333334 = -1.943650632 Reorder the terms: -1.333333334 + w = -1.943650632 Solving -1.333333334 + w = -1.943650632 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + w = -1.943650632 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + w = -1.943650632 + 1.333333334 w = -1.943650632 + 1.333333334 Combine like terms: -1.943650632 + 1.333333334 = -0.610317298 w = -0.610317298 Simplifying w = -0.610317298Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.276983966, -0.610317298}Solution
w = {3.276983966, -0.610317298}
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