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Simplifying 21w + 30 = 3w2 Reorder the terms: 30 + 21w = 3w2 Solving 30 + 21w = 3w2 Solving for variable 'w'. Combine like terms: 3w2 + -3w2 = 0 30 + 21w + -3w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 7w + -1w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + 7w + -1w2)' equal to zero and attempt to solve: Simplifying 10 + 7w + -1w2 = 0 Solving 10 + 7w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -7w + w2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -7w + 10 + w2 = 0 + 10 Reorder the terms: -10 + 10 + -7w + w2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -7w + w2 = 0 + 10 -7w + w2 = 0 + 10 Combine like terms: 0 + 10 = 10 -7w + w2 = 10 The w term is -7w. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7w + 12.25 + w2 = 10 + 12.25 Reorder the terms: 12.25 + -7w + w2 = 10 + 12.25 Combine like terms: 10 + 12.25 = 22.25 12.25 + -7w + w2 = 22.25 Factor a perfect square on the left side: (w + -3.5)(w + -3.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (w + -3.5) equal to 4.716990566 and -4.716990566.Subproblem 1
w + -3.5 = 4.716990566 Simplifying w + -3.5 = 4.716990566 Reorder the terms: -3.5 + w = 4.716990566 Solving -3.5 + w = 4.716990566 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + w = 4.716990566 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + w = 4.716990566 + 3.5 w = 4.716990566 + 3.5 Combine like terms: 4.716990566 + 3.5 = 8.216990566 w = 8.216990566 Simplifying w = 8.216990566Subproblem 2
w + -3.5 = -4.716990566 Simplifying w + -3.5 = -4.716990566 Reorder the terms: -3.5 + w = -4.716990566 Solving -3.5 + w = -4.716990566 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + w = -4.716990566 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + w = -4.716990566 + 3.5 w = -4.716990566 + 3.5 Combine like terms: -4.716990566 + 3.5 = -1.216990566 w = -1.216990566 Simplifying w = -1.216990566Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.216990566, -1.216990566}Solution
w = {8.216990566, -1.216990566}
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