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Simplifying 16w2 + -18w + 1 = 0 Reorder the terms: 1 + -18w + 16w2 = 0 Solving 1 + -18w + 16w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -1.125w + w2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -1.125w + -0.0625 + w2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -1.125w + w2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -1.125w + w2 = 0 + -0.0625 -1.125w + w2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -1.125w + w2 = -0.0625 The w term is -1.125w. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125w + 0.31640625 + w2 = -0.0625 + 0.31640625 Reorder the terms: 0.31640625 + -1.125w + w2 = -0.0625 + 0.31640625 Combine like terms: -0.0625 + 0.31640625 = 0.25390625 0.31640625 + -1.125w + w2 = 0.25390625 Factor a perfect square on the left side: (w + -0.5625)(w + -0.5625) = 0.25390625 Calculate the square root of the right side: 0.503891109 Break this problem into two subproblems by setting (w + -0.5625) equal to 0.503891109 and -0.503891109.Subproblem 1
w + -0.5625 = 0.503891109 Simplifying w + -0.5625 = 0.503891109 Reorder the terms: -0.5625 + w = 0.503891109 Solving -0.5625 + w = 0.503891109 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + w = 0.503891109 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + w = 0.503891109 + 0.5625 w = 0.503891109 + 0.5625 Combine like terms: 0.503891109 + 0.5625 = 1.066391109 w = 1.066391109 Simplifying w = 1.066391109Subproblem 2
w + -0.5625 = -0.503891109 Simplifying w + -0.5625 = -0.503891109 Reorder the terms: -0.5625 + w = -0.503891109 Solving -0.5625 + w = -0.503891109 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + w = -0.503891109 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + w = -0.503891109 + 0.5625 w = -0.503891109 + 0.5625 Combine like terms: -0.503891109 + 0.5625 = 0.058608891 w = 0.058608891 Simplifying w = 0.058608891Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.066391109, 0.058608891}
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