26=6(w+7)2w

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Solution for 26=6(w+7)2w equation:


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 = 0.296928583

Subproblem 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 = -7.296928583

Solution

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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