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Simplifying 4(w + -9) * 7w = 52 Reorder the terms: 4(-9 + w) * 7w = 52 Reorder the terms for easier multiplication: 4 * 7w(-9 + w) = 52 Multiply 4 * 7 28w(-9 + w) = 52 (-9 * 28w + w * 28w) = 52 (-252w + 28w2) = 52 Solving -252w + 28w2 = 52 Solving for variable 'w'. Reorder the terms: -52 + -252w + 28w2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + -252w + 28w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-13 + -63w + 7w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-13 + -63w + 7w2)' equal to zero and attempt to solve: Simplifying -13 + -63w + 7w2 = 0 Solving -13 + -63w + 7w2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + -9w + w2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + -9w + 1.857142857 + w2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + -9w + w2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + -9w + w2 = 0 + 1.857142857 -9w + w2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 -9w + w2 = 1.857142857 The w term is -9w. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9w + 20.25 + w2 = 1.857142857 + 20.25 Reorder the terms: 20.25 + -9w + w2 = 1.857142857 + 20.25 Combine like terms: 1.857142857 + 20.25 = 22.107142857 20.25 + -9w + w2 = 22.107142857 Factor a perfect square on the left side: (w + -4.5)(w + -4.5) = 22.107142857 Calculate the square root of the right side: 4.701823355 Break this problem into two subproblems by setting (w + -4.5) equal to 4.701823355 and -4.701823355.Subproblem 1
w + -4.5 = 4.701823355 Simplifying w + -4.5 = 4.701823355 Reorder the terms: -4.5 + w = 4.701823355 Solving -4.5 + w = 4.701823355 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + w = 4.701823355 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = 4.701823355 + 4.5 w = 4.701823355 + 4.5 Combine like terms: 4.701823355 + 4.5 = 9.201823355 w = 9.201823355 Simplifying w = 9.201823355Subproblem 2
w + -4.5 = -4.701823355 Simplifying w + -4.5 = -4.701823355 Reorder the terms: -4.5 + w = -4.701823355 Solving -4.5 + w = -4.701823355 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + w = -4.701823355 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = -4.701823355 + 4.5 w = -4.701823355 + 4.5 Combine like terms: -4.701823355 + 4.5 = -0.201823355 w = -0.201823355 Simplifying w = -0.201823355Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.201823355, -0.201823355}Solution
w = {9.201823355, -0.201823355}
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