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Simplifying 10w + -1w2 = 15 Solving 10w + -1w2 = 15 Solving for variable 'w'. Reorder the terms: -15 + 10w + -1w2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 10w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 15 + -10w + w2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -10w + -15 + w2 = 0 + -15 Reorder the terms: 15 + -15 + -10w + w2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -10w + w2 = 0 + -15 -10w + w2 = 0 + -15 Combine like terms: 0 + -15 = -15 -10w + w2 = -15 The w term is -10w. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10w + 25 + w2 = -15 + 25 Reorder the terms: 25 + -10w + w2 = -15 + 25 Combine like terms: -15 + 25 = 10 25 + -10w + w2 = 10 Factor a perfect square on the left side: (w + -5)(w + -5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (w + -5) equal to 3.16227766 and -3.16227766.Subproblem 1
w + -5 = 3.16227766 Simplifying w + -5 = 3.16227766 Reorder the terms: -5 + w = 3.16227766 Solving -5 + w = 3.16227766 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 3.16227766 + 5 Combine like terms: -5 + 5 = 0 0 + w = 3.16227766 + 5 w = 3.16227766 + 5 Combine like terms: 3.16227766 + 5 = 8.16227766 w = 8.16227766 Simplifying w = 8.16227766Subproblem 2
w + -5 = -3.16227766 Simplifying w + -5 = -3.16227766 Reorder the terms: -5 + w = -3.16227766 Solving -5 + w = -3.16227766 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = -3.16227766 + 5 Combine like terms: -5 + 5 = 0 0 + w = -3.16227766 + 5 w = -3.16227766 + 5 Combine like terms: -3.16227766 + 5 = 1.83772234 w = 1.83772234 Simplifying w = 1.83772234Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.16227766, 1.83772234}
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