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Simplifying (w2 + -10w + 5) + -1(-4w2 + -10w + 4) + (-3w + 9w + -7) = 0 Reorder the terms: (5 + -10w + w2) + -1(-4w2 + -10w + 4) + (-3w + 9w + -7) = 0 Remove parenthesis around (5 + -10w + w2) 5 + -10w + w2 + -1(-4w2 + -10w + 4) + (-3w + 9w + -7) = 0 Reorder the terms: 5 + -10w + w2 + -1(4 + -10w + -4w2) + (-3w + 9w + -7) = 0 5 + -10w + w2 + (4 * -1 + -10w * -1 + -4w2 * -1) + (-3w + 9w + -7) = 0 5 + -10w + w2 + (-4 + 10w + 4w2) + (-3w + 9w + -7) = 0 Reorder the terms: 5 + -10w + w2 + -4 + 10w + 4w2 + (-7 + -3w + 9w) = 0 Combine like terms: -3w + 9w = 6w 5 + -10w + w2 + -4 + 10w + 4w2 + (-7 + 6w) = 0 Remove parenthesis around (-7 + 6w) 5 + -10w + w2 + -4 + 10w + 4w2 + -7 + 6w = 0 Reorder the terms: 5 + -4 + -7 + -10w + 10w + 6w + w2 + 4w2 = 0 Combine like terms: 5 + -4 = 1 1 + -7 + -10w + 10w + 6w + w2 + 4w2 = 0 Combine like terms: 1 + -7 = -6 -6 + -10w + 10w + 6w + w2 + 4w2 = 0 Combine like terms: -10w + 10w = 0 -6 + 0 + 6w + w2 + 4w2 = 0 -6 + 6w + w2 + 4w2 = 0 Combine like terms: w2 + 4w2 = 5w2 -6 + 6w + 5w2 = 0 Solving -6 + 6w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 1.2w + w2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 1.2w + 1.2 + w2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 1.2w + w2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 1.2w + w2 = 0 + 1.2 1.2w + w2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 1.2w + w2 = 1.2 The w term is 1.2w. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2w + 0.36 + w2 = 1.2 + 0.36 Reorder the terms: 0.36 + 1.2w + w2 = 1.2 + 0.36 Combine like terms: 1.2 + 0.36 = 1.56 0.36 + 1.2w + w2 = 1.56 Factor a perfect square on the left side: (w + 0.6)(w + 0.6) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (w + 0.6) equal to 1.2489996 and -1.2489996.Subproblem 1
w + 0.6 = 1.2489996 Simplifying w + 0.6 = 1.2489996 Reorder the terms: 0.6 + w = 1.2489996 Solving 0.6 + w = 1.2489996 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + w = 1.2489996 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + w = 1.2489996 + -0.6 w = 1.2489996 + -0.6 Combine like terms: 1.2489996 + -0.6 = 0.6489996 w = 0.6489996 Simplifying w = 0.6489996Subproblem 2
w + 0.6 = -1.2489996 Simplifying w + 0.6 = -1.2489996 Reorder the terms: 0.6 + w = -1.2489996 Solving 0.6 + w = -1.2489996 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + w = -1.2489996 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + w = -1.2489996 + -0.6 w = -1.2489996 + -0.6 Combine like terms: -1.2489996 + -0.6 = -1.8489996 w = -1.8489996 Simplifying w = -1.8489996Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.6489996, -1.8489996}
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