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Simplifying 24w = 6w2 + -12 Reorder the terms: 24w = -12 + 6w2 Solving 24w = -12 + 6w2 Solving for variable 'w'. Reorder the terms: 12 + 24w + -6w2 = -12 + 6w2 + 12 + -6w2 Reorder the terms: 12 + 24w + -6w2 = -12 + 12 + 6w2 + -6w2 Combine like terms: -12 + 12 = 0 12 + 24w + -6w2 = 0 + 6w2 + -6w2 12 + 24w + -6w2 = 6w2 + -6w2 Combine like terms: 6w2 + -6w2 = 0 12 + 24w + -6w2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(2 + 4w + -1w2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + 4w + -1w2)' equal to zero and attempt to solve: Simplifying 2 + 4w + -1w2 = 0 Solving 2 + 4w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -4w + w2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -4w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + -4w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4w + w2 = 0 + 2 -4w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4w + w2 = 2 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 2 + 4 Reorder the terms: 4 + -4w + w2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4w + w2 = 6 Factor a perfect square on the left side: (w + -2)(w + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (w + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
w + -2 = 2.449489743 Simplifying w + -2 = 2.449489743 Reorder the terms: -2 + w = 2.449489743 Solving -2 + w = 2.449489743 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + w = 2.449489743 + 2 w = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 w = 4.449489743 Simplifying w = 4.449489743Subproblem 2
w + -2 = -2.449489743 Simplifying w + -2 = -2.449489743 Reorder the terms: -2 + w = -2.449489743 Solving -2 + w = -2.449489743 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + w = -2.449489743 + 2 w = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 w = -0.449489743 Simplifying w = -0.449489743Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.449489743, -0.449489743}Solution
w = {4.449489743, -0.449489743}
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