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Simplifying 2w2 + 6w + -870 = 0 Reorder the terms: -870 + 6w + 2w2 = 0 Solving -870 + 6w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-435 + 3w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-435 + 3w + w2)' equal to zero and attempt to solve: Simplifying -435 + 3w + w2 = 0 Solving -435 + 3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '435' to each side of the equation. -435 + 3w + 435 + w2 = 0 + 435 Reorder the terms: -435 + 435 + 3w + w2 = 0 + 435 Combine like terms: -435 + 435 = 0 0 + 3w + w2 = 0 + 435 3w + w2 = 0 + 435 Combine like terms: 0 + 435 = 435 3w + w2 = 435 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 435 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 435 + 2.25 Combine like terms: 435 + 2.25 = 437.25 2.25 + 3w + w2 = 437.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 437.25 Calculate the square root of the right side: 20.910523666 Break this problem into two subproblems by setting (w + 1.5) equal to 20.910523666 and -20.910523666.Subproblem 1
w + 1.5 = 20.910523666 Simplifying w + 1.5 = 20.910523666 Reorder the terms: 1.5 + w = 20.910523666 Solving 1.5 + w = 20.910523666 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 20.910523666 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 20.910523666 + -1.5 w = 20.910523666 + -1.5 Combine like terms: 20.910523666 + -1.5 = 19.410523666 w = 19.410523666 Simplifying w = 19.410523666Subproblem 2
w + 1.5 = -20.910523666 Simplifying w + 1.5 = -20.910523666 Reorder the terms: 1.5 + w = -20.910523666 Solving 1.5 + w = -20.910523666 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -20.910523666 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -20.910523666 + -1.5 w = -20.910523666 + -1.5 Combine like terms: -20.910523666 + -1.5 = -22.410523666 w = -22.410523666 Simplifying w = -22.410523666Solution
The solution to the problem is based on the solutions from the subproblems. w = {19.410523666, -22.410523666}Solution
w = {19.410523666, -22.410523666}
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