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Simplifying (-7w2 + 2w + -5) + (4w2 + 3w + 6) = 0 Reorder the terms: (-5 + 2w + -7w2) + (4w2 + 3w + 6) = 0 Remove parenthesis around (-5 + 2w + -7w2) -5 + 2w + -7w2 + (4w2 + 3w + 6) = 0 Reorder the terms: -5 + 2w + -7w2 + (6 + 3w + 4w2) = 0 Remove parenthesis around (6 + 3w + 4w2) -5 + 2w + -7w2 + 6 + 3w + 4w2 = 0 Reorder the terms: -5 + 6 + 2w + 3w + -7w2 + 4w2 = 0 Combine like terms: -5 + 6 = 1 1 + 2w + 3w + -7w2 + 4w2 = 0 Combine like terms: 2w + 3w = 5w 1 + 5w + -7w2 + 4w2 = 0 Combine like terms: -7w2 + 4w2 = -3w2 1 + 5w + -3w2 = 0 Solving 1 + 5w + -3w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.3333333333 + -1.666666667w + w2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.666666667w + 0.3333333333 + w2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.666666667w + w2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.666666667w + w2 = 0 + 0.3333333333 -1.666666667w + w2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.666666667w + w2 = 0.3333333333 The w term is -1.666666667w. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667w + 0.6944444447 + w2 = 0.3333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667w + w2 = 0.3333333333 + 0.6944444447 Combine like terms: 0.3333333333 + 0.6944444447 = 1.027777778 0.6944444447 + -1.666666667w + w2 = 1.027777778 Factor a perfect square on the left side: (w + -0.8333333335)(w + -0.8333333335) = 1.027777778 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (w + -0.8333333335) equal to 1.013793755 and -1.013793755.Subproblem 1
w + -0.8333333335 = 1.013793755 Simplifying w + -0.8333333335 = 1.013793755 Reorder the terms: -0.8333333335 + w = 1.013793755 Solving -0.8333333335 + w = 1.013793755 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + w = 1.013793755 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + w = 1.013793755 + 0.8333333335 w = 1.013793755 + 0.8333333335 Combine like terms: 1.013793755 + 0.8333333335 = 1.8471270885 w = 1.8471270885 Simplifying w = 1.8471270885Subproblem 2
w + -0.8333333335 = -1.013793755 Simplifying w + -0.8333333335 = -1.013793755 Reorder the terms: -0.8333333335 + w = -1.013793755 Solving -0.8333333335 + w = -1.013793755 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + w = -1.013793755 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + w = -1.013793755 + 0.8333333335 w = -1.013793755 + 0.8333333335 Combine like terms: -1.013793755 + 0.8333333335 = -0.1804604215 w = -0.1804604215 Simplifying w = -0.1804604215Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.8471270885, -0.1804604215}
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