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Simplifying 10w2 + 13w + -15 = 0 Reorder the terms: -15 + 13w + 10w2 = 0 Solving -15 + 13w + 10w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + 1.3w + w2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 1.3w + 1.5 + w2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 1.3w + w2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 1.3w + w2 = 0 + 1.5 1.3w + w2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 1.3w + w2 = 1.5 The w term is 1.3w. Take half its coefficient (0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. 1.3w + 0.4225 + w2 = 1.5 + 0.4225 Reorder the terms: 0.4225 + 1.3w + w2 = 1.5 + 0.4225 Combine like terms: 1.5 + 0.4225 = 1.9225 0.4225 + 1.3w + w2 = 1.9225 Factor a perfect square on the left side: (w + 0.65)(w + 0.65) = 1.9225 Calculate the square root of the right side: 1.386542462 Break this problem into two subproblems by setting (w + 0.65) equal to 1.386542462 and -1.386542462.Subproblem 1
w + 0.65 = 1.386542462 Simplifying w + 0.65 = 1.386542462 Reorder the terms: 0.65 + w = 1.386542462 Solving 0.65 + w = 1.386542462 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + w = 1.386542462 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + w = 1.386542462 + -0.65 w = 1.386542462 + -0.65 Combine like terms: 1.386542462 + -0.65 = 0.736542462 w = 0.736542462 Simplifying w = 0.736542462Subproblem 2
w + 0.65 = -1.386542462 Simplifying w + 0.65 = -1.386542462 Reorder the terms: 0.65 + w = -1.386542462 Solving 0.65 + w = -1.386542462 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + w = -1.386542462 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + w = -1.386542462 + -0.65 w = -1.386542462 + -0.65 Combine like terms: -1.386542462 + -0.65 = -2.036542462 w = -2.036542462 Simplifying w = -2.036542462Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.736542462, -2.036542462}
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