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Simplifying w2 + -28w + 91 = 0 Reorder the terms: 91 + -28w + w2 = 0 Solving 91 + -28w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-91' to each side of the equation. 91 + -28w + -91 + w2 = 0 + -91 Reorder the terms: 91 + -91 + -28w + w2 = 0 + -91 Combine like terms: 91 + -91 = 0 0 + -28w + w2 = 0 + -91 -28w + w2 = 0 + -91 Combine like terms: 0 + -91 = -91 -28w + w2 = -91 The w term is -28w. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28w + 196 + w2 = -91 + 196 Reorder the terms: 196 + -28w + w2 = -91 + 196 Combine like terms: -91 + 196 = 105 196 + -28w + w2 = 105 Factor a perfect square on the left side: (w + -14)(w + -14) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (w + -14) equal to 10.246950766 and -10.246950766.Subproblem 1
w + -14 = 10.246950766 Simplifying w + -14 = 10.246950766 Reorder the terms: -14 + w = 10.246950766 Solving -14 + w = 10.246950766 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + w = 10.246950766 + 14 Combine like terms: -14 + 14 = 0 0 + w = 10.246950766 + 14 w = 10.246950766 + 14 Combine like terms: 10.246950766 + 14 = 24.246950766 w = 24.246950766 Simplifying w = 24.246950766Subproblem 2
w + -14 = -10.246950766 Simplifying w + -14 = -10.246950766 Reorder the terms: -14 + w = -10.246950766 Solving -14 + w = -10.246950766 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + w = -10.246950766 + 14 Combine like terms: -14 + 14 = 0 0 + w = -10.246950766 + 14 w = -10.246950766 + 14 Combine like terms: -10.246950766 + 14 = 3.753049234 w = 3.753049234 Simplifying w = 3.753049234Solution
The solution to the problem is based on the solutions from the subproblems. w = {24.246950766, 3.753049234}
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