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Simplifying w2 + -21w + 15 = 0 Reorder the terms: 15 + -21w + w2 = 0 Solving 15 + -21w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -21w + -15 + w2 = 0 + -15 Reorder the terms: 15 + -15 + -21w + w2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -21w + w2 = 0 + -15 -21w + w2 = 0 + -15 Combine like terms: 0 + -15 = -15 -21w + w2 = -15 The w term is -21w. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21w + 110.25 + w2 = -15 + 110.25 Reorder the terms: 110.25 + -21w + w2 = -15 + 110.25 Combine like terms: -15 + 110.25 = 95.25 110.25 + -21w + w2 = 95.25 Factor a perfect square on the left side: (w + -10.5)(w + -10.5) = 95.25 Calculate the square root of the right side: 9.759610648 Break this problem into two subproblems by setting (w + -10.5) equal to 9.759610648 and -9.759610648.Subproblem 1
w + -10.5 = 9.759610648 Simplifying w + -10.5 = 9.759610648 Reorder the terms: -10.5 + w = 9.759610648 Solving -10.5 + w = 9.759610648 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + w = 9.759610648 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + w = 9.759610648 + 10.5 w = 9.759610648 + 10.5 Combine like terms: 9.759610648 + 10.5 = 20.259610648 w = 20.259610648 Simplifying w = 20.259610648Subproblem 2
w + -10.5 = -9.759610648 Simplifying w + -10.5 = -9.759610648 Reorder the terms: -10.5 + w = -9.759610648 Solving -10.5 + w = -9.759610648 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + w = -9.759610648 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + w = -9.759610648 + 10.5 w = -9.759610648 + 10.5 Combine like terms: -9.759610648 + 10.5 = 0.740389352 w = 0.740389352 Simplifying w = 0.740389352Solution
The solution to the problem is based on the solutions from the subproblems. w = {20.259610648, 0.740389352}
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