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Simplifying 2w(2w) + -13w = 7 Remove parenthesis around (2w) 2w * 2w + -13w = 7 Reorder the terms for easier multiplication: 2 * 2w * w + -13w = 7 Multiply 2 * 2 4w * w + -13w = 7 Multiply w * w 4w2 + -13w = 7 Reorder the terms: -13w + 4w2 = 7 Solving -13w + 4w2 = 7 Solving for variable 'w'. Reorder the terms: -7 + -13w + 4w2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -13w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -3.25w + w2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -3.25w + 1.75 + w2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -3.25w + w2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -3.25w + w2 = 0 + 1.75 -3.25w + w2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -3.25w + w2 = 1.75 The w term is -3.25w. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25w + 2.640625 + w2 = 1.75 + 2.640625 Reorder the terms: 2.640625 + -3.25w + w2 = 1.75 + 2.640625 Combine like terms: 1.75 + 2.640625 = 4.390625 2.640625 + -3.25w + w2 = 4.390625 Factor a perfect square on the left side: (w + -1.625)(w + -1.625) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (w + -1.625) equal to 2.095381827 and -2.095381827.Subproblem 1
w + -1.625 = 2.095381827 Simplifying w + -1.625 = 2.095381827 Reorder the terms: -1.625 + w = 2.095381827 Solving -1.625 + w = 2.095381827 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + w = 2.095381827 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + w = 2.095381827 + 1.625 w = 2.095381827 + 1.625 Combine like terms: 2.095381827 + 1.625 = 3.720381827 w = 3.720381827 Simplifying w = 3.720381827Subproblem 2
w + -1.625 = -2.095381827 Simplifying w + -1.625 = -2.095381827 Reorder the terms: -1.625 + w = -2.095381827 Solving -1.625 + w = -2.095381827 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + w = -2.095381827 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + w = -2.095381827 + 1.625 w = -2.095381827 + 1.625 Combine like terms: -2.095381827 + 1.625 = -0.470381827 w = -0.470381827 Simplifying w = -0.470381827Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.720381827, -0.470381827}
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