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Simplifying (-5w2 + -1w + 4) + (-6w2 + 7) = 0 Reorder the terms: (4 + -1w + -5w2) + (-6w2 + 7) = 0 Remove parenthesis around (4 + -1w + -5w2) 4 + -1w + -5w2 + (-6w2 + 7) = 0 Reorder the terms: 4 + -1w + -5w2 + (7 + -6w2) = 0 Remove parenthesis around (7 + -6w2) 4 + -1w + -5w2 + 7 + -6w2 = 0 Reorder the terms: 4 + 7 + -1w + -5w2 + -6w2 = 0 Combine like terms: 4 + 7 = 11 11 + -1w + -5w2 + -6w2 = 0 Combine like terms: -5w2 + -6w2 = -11w2 11 + -1w + -11w2 = 0 Solving 11 + -1w + -11w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -1 + 0.09090909091w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.09090909091w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + 0.09090909091w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.09090909091w + w2 = 0 + 1 0.09090909091w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.09090909091w + w2 = 1 The w term is 0.09090909091w. Take half its coefficient (0.04545454546). Square it (0.002066115703) and add it to both sides. Add '0.002066115703' to each side of the equation. 0.09090909091w + 0.002066115703 + w2 = 1 + 0.002066115703 Reorder the terms: 0.002066115703 + 0.09090909091w + w2 = 1 + 0.002066115703 Combine like terms: 1 + 0.002066115703 = 1.002066115703 0.002066115703 + 0.09090909091w + w2 = 1.002066115703 Factor a perfect square on the left side: (w + 0.04545454546)(w + 0.04545454546) = 1.002066115703 Calculate the square root of the right side: 1.001032525 Break this problem into two subproblems by setting (w + 0.04545454546) equal to 1.001032525 and -1.001032525.Subproblem 1
w + 0.04545454546 = 1.001032525 Simplifying w + 0.04545454546 = 1.001032525 Reorder the terms: 0.04545454546 + w = 1.001032525 Solving 0.04545454546 + w = 1.001032525 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.04545454546' to each side of the equation. 0.04545454546 + -0.04545454546 + w = 1.001032525 + -0.04545454546 Combine like terms: 0.04545454546 + -0.04545454546 = 0.00000000000 0.00000000000 + w = 1.001032525 + -0.04545454546 w = 1.001032525 + -0.04545454546 Combine like terms: 1.001032525 + -0.04545454546 = 0.95557797954 w = 0.95557797954 Simplifying w = 0.95557797954Subproblem 2
w + 0.04545454546 = -1.001032525 Simplifying w + 0.04545454546 = -1.001032525 Reorder the terms: 0.04545454546 + w = -1.001032525 Solving 0.04545454546 + w = -1.001032525 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.04545454546' to each side of the equation. 0.04545454546 + -0.04545454546 + w = -1.001032525 + -0.04545454546 Combine like terms: 0.04545454546 + -0.04545454546 = 0.00000000000 0.00000000000 + w = -1.001032525 + -0.04545454546 w = -1.001032525 + -0.04545454546 Combine like terms: -1.001032525 + -0.04545454546 = -1.04648707046 w = -1.04648707046 Simplifying w = -1.04648707046Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.95557797954, -1.04648707046}
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