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Simplifying -1w + 21w2 + -104 = 0 Reorder the terms: -104 + -1w + 21w2 = 0 Solving -104 + -1w + 21w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -4.952380952 + -0.04761904762w + w2 = 0 Move the constant term to the right: Add '4.952380952' to each side of the equation. -4.952380952 + -0.04761904762w + 4.952380952 + w2 = 0 + 4.952380952 Reorder the terms: -4.952380952 + 4.952380952 + -0.04761904762w + w2 = 0 + 4.952380952 Combine like terms: -4.952380952 + 4.952380952 = 0.000000000 0.000000000 + -0.04761904762w + w2 = 0 + 4.952380952 -0.04761904762w + w2 = 0 + 4.952380952 Combine like terms: 0 + 4.952380952 = 4.952380952 -0.04761904762w + w2 = 4.952380952 The w term is -0.04761904762w. Take half its coefficient (-0.02380952381). Square it (0.0005668934241) and add it to both sides. Add '0.0005668934241' to each side of the equation. -0.04761904762w + 0.0005668934241 + w2 = 4.952380952 + 0.0005668934241 Reorder the terms: 0.0005668934241 + -0.04761904762w + w2 = 4.952380952 + 0.0005668934241 Combine like terms: 4.952380952 + 0.0005668934241 = 4.9529478454241 0.0005668934241 + -0.04761904762w + w2 = 4.9529478454241 Factor a perfect square on the left side: (w + -0.02380952381)(w + -0.02380952381) = 4.9529478454241 Calculate the square root of the right side: 2.225521927 Break this problem into two subproblems by setting (w + -0.02380952381) equal to 2.225521927 and -2.225521927.Subproblem 1
w + -0.02380952381 = 2.225521927 Simplifying w + -0.02380952381 = 2.225521927 Reorder the terms: -0.02380952381 + w = 2.225521927 Solving -0.02380952381 + w = 2.225521927 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.02380952381' to each side of the equation. -0.02380952381 + 0.02380952381 + w = 2.225521927 + 0.02380952381 Combine like terms: -0.02380952381 + 0.02380952381 = 0.00000000000 0.00000000000 + w = 2.225521927 + 0.02380952381 w = 2.225521927 + 0.02380952381 Combine like terms: 2.225521927 + 0.02380952381 = 2.24933145081 w = 2.24933145081 Simplifying w = 2.24933145081Subproblem 2
w + -0.02380952381 = -2.225521927 Simplifying w + -0.02380952381 = -2.225521927 Reorder the terms: -0.02380952381 + w = -2.225521927 Solving -0.02380952381 + w = -2.225521927 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.02380952381' to each side of the equation. -0.02380952381 + 0.02380952381 + w = -2.225521927 + 0.02380952381 Combine like terms: -0.02380952381 + 0.02380952381 = 0.00000000000 0.00000000000 + w = -2.225521927 + 0.02380952381 w = -2.225521927 + 0.02380952381 Combine like terms: -2.225521927 + 0.02380952381 = -2.20171240319 w = -2.20171240319 Simplifying w = -2.20171240319Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.24933145081, -2.20171240319}
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