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Simplifying 26 = 6(w + 7) * 2w Reorder the terms: 26 = 6(7 + w) * 2w Reorder the terms for easier multiplication: 26 = 6 * 2w(7 + w) Multiply 6 * 2 26 = 12w(7 + w) 26 = (7 * 12w + w * 12w) 26 = (84w + 12w2) Solving 26 = 84w + 12w2 Solving for variable 'w'. Reorder the terms: 26 + -84w + -12w2 = 84w + -84w + 12w2 + -12w2 Combine like terms: 84w + -84w = 0 26 + -84w + -12w2 = 0 + 12w2 + -12w2 26 + -84w + -12w2 = 12w2 + -12w2 Combine like terms: 12w2 + -12w2 = 0 26 + -84w + -12w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -42w + -6w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -42w + -6w2)' equal to zero and attempt to solve: Simplifying 13 + -42w + -6w2 = 0 Solving 13 + -42w + -6w2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2.166666667 + 7w + w2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + 7w + 2.166666667 + w2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + 7w + w2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + 7w + w2 = 0 + 2.166666667 7w + w2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 7w + w2 = 2.166666667 The w term is 7w. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7w + 12.25 + w2 = 2.166666667 + 12.25 Reorder the terms: 12.25 + 7w + w2 = 2.166666667 + 12.25 Combine like terms: 2.166666667 + 12.25 = 14.416666667 12.25 + 7w + w2 = 14.416666667 Factor a perfect square on the left side: (w + 3.5)(w + 3.5) = 14.416666667 Calculate the square root of the right side: 3.796928583 Break this problem into two subproblems by setting (w + 3.5) equal to 3.796928583 and -3.796928583.Subproblem 1
w + 3.5 = 3.796928583 Simplifying w + 3.5 = 3.796928583 Reorder the terms: 3.5 + w = 3.796928583 Solving 3.5 + w = 3.796928583 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = 3.796928583 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 3.796928583 + -3.5 w = 3.796928583 + -3.5 Combine like terms: 3.796928583 + -3.5 = 0.296928583 w = 0.296928583 Simplifying w = 0.296928583Subproblem 2
w + 3.5 = -3.796928583 Simplifying w + 3.5 = -3.796928583 Reorder the terms: 3.5 + w = -3.796928583 Solving 3.5 + w = -3.796928583 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = -3.796928583 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -3.796928583 + -3.5 w = -3.796928583 + -3.5 Combine like terms: -3.796928583 + -3.5 = -7.296928583 w = -7.296928583 Simplifying w = -7.296928583Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.296928583, -7.296928583}Solution
w = {0.296928583, -7.296928583}
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