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Simplifying 2w2 + -3w + -140 = 0 Reorder the terms: -140 + -3w + 2w2 = 0 Solving -140 + -3w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -70 + -1.5w + w2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + -1.5w + 70 + w2 = 0 + 70 Reorder the terms: -70 + 70 + -1.5w + w2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -1.5w + w2 = 0 + 70 -1.5w + w2 = 0 + 70 Combine like terms: 0 + 70 = 70 -1.5w + w2 = 70 The w term is -1.5w. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5w + 0.5625 + w2 = 70 + 0.5625 Reorder the terms: 0.5625 + -1.5w + w2 = 70 + 0.5625 Combine like terms: 70 + 0.5625 = 70.5625 0.5625 + -1.5w + w2 = 70.5625 Factor a perfect square on the left side: (w + -0.75)(w + -0.75) = 70.5625 Calculate the square root of the right side: 8.400148808 Break this problem into two subproblems by setting (w + -0.75) equal to 8.400148808 and -8.400148808.Subproblem 1
w + -0.75 = 8.400148808 Simplifying w + -0.75 = 8.400148808 Reorder the terms: -0.75 + w = 8.400148808 Solving -0.75 + w = 8.400148808 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + w = 8.400148808 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = 8.400148808 + 0.75 w = 8.400148808 + 0.75 Combine like terms: 8.400148808 + 0.75 = 9.150148808 w = 9.150148808 Simplifying w = 9.150148808Subproblem 2
w + -0.75 = -8.400148808 Simplifying w + -0.75 = -8.400148808 Reorder the terms: -0.75 + w = -8.400148808 Solving -0.75 + w = -8.400148808 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + w = -8.400148808 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = -8.400148808 + 0.75 w = -8.400148808 + 0.75 Combine like terms: -8.400148808 + 0.75 = -7.650148808 w = -7.650148808 Simplifying w = -7.650148808Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.150148808, -7.650148808}
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