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Simplifying (w2 + -5w + -6) + (3w2 + -4w + 2) = 0 Reorder the terms: (-6 + -5w + w2) + (3w2 + -4w + 2) = 0 Remove parenthesis around (-6 + -5w + w2) -6 + -5w + w2 + (3w2 + -4w + 2) = 0 Reorder the terms: -6 + -5w + w2 + (2 + -4w + 3w2) = 0 Remove parenthesis around (2 + -4w + 3w2) -6 + -5w + w2 + 2 + -4w + 3w2 = 0 Reorder the terms: -6 + 2 + -5w + -4w + w2 + 3w2 = 0 Combine like terms: -6 + 2 = -4 -4 + -5w + -4w + w2 + 3w2 = 0 Combine like terms: -5w + -4w = -9w -4 + -9w + w2 + 3w2 = 0 Combine like terms: w2 + 3w2 = 4w2 -4 + -9w + 4w2 = 0 Solving -4 + -9w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -2.25w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.25w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -2.25w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.25w + w2 = 0 + 1 -2.25w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.25w + w2 = 1 The w term is -2.25w. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25w + 1.265625 + w2 = 1 + 1.265625 Reorder the terms: 1.265625 + -2.25w + w2 = 1 + 1.265625 Combine like terms: 1 + 1.265625 = 2.265625 1.265625 + -2.25w + w2 = 2.265625 Factor a perfect square on the left side: (w + -1.125)(w + -1.125) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (w + -1.125) equal to 1.505199322 and -1.505199322.Subproblem 1
w + -1.125 = 1.505199322 Simplifying w + -1.125 = 1.505199322 Reorder the terms: -1.125 + w = 1.505199322 Solving -1.125 + w = 1.505199322 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + w = 1.505199322 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + w = 1.505199322 + 1.125 w = 1.505199322 + 1.125 Combine like terms: 1.505199322 + 1.125 = 2.630199322 w = 2.630199322 Simplifying w = 2.630199322Subproblem 2
w + -1.125 = -1.505199322 Simplifying w + -1.125 = -1.505199322 Reorder the terms: -1.125 + w = -1.505199322 Solving -1.125 + w = -1.505199322 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + w = -1.505199322 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + w = -1.505199322 + 1.125 w = -1.505199322 + 1.125 Combine like terms: -1.505199322 + 1.125 = -0.380199322 w = -0.380199322 Simplifying w = -0.380199322Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.630199322, -0.380199322}
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