2w^2+12w-36=0

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Solution for 2w^2+12w-36=0 equation:


Simplifying
2w2 + 12w + -36 = 0

Reorder the terms:
-36 + 12w + 2w2 = 0

Solving
-36 + 12w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 6w + w2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-18 + 6w + w2)' equal to zero and attempt to solve: Simplifying -18 + 6w + w2 = 0 Solving -18 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 6w + 18 + w2 = 0 + 18 Reorder the terms: -18 + 18 + 6w + w2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 6w + w2 = 0 + 18 6w + w2 = 0 + 18 Combine like terms: 0 + 18 = 18 6w + w2 = 18 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 18 + 9 Reorder the terms: 9 + 6w + w2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + 6w + w2 = 27 Factor a perfect square on the left side: (w + 3)(w + 3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (w + 3) equal to 5.196152423 and -5.196152423.

Subproblem 1

w + 3 = 5.196152423 Simplifying w + 3 = 5.196152423 Reorder the terms: 3 + w = 5.196152423 Solving 3 + w = 5.196152423 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + w = 5.196152423 + -3 w = 5.196152423 + -3 Combine like terms: 5.196152423 + -3 = 2.196152423 w = 2.196152423 Simplifying w = 2.196152423

Subproblem 2

w + 3 = -5.196152423 Simplifying w + 3 = -5.196152423 Reorder the terms: 3 + w = -5.196152423 Solving 3 + w = -5.196152423 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + w = -5.196152423 + -3 w = -5.196152423 + -3 Combine like terms: -5.196152423 + -3 = -8.196152423 w = -8.196152423 Simplifying w = -8.196152423

Solution

The solution to the problem is based on the solutions from the subproblems. w = {2.196152423, -8.196152423}

Solution

w = {2.196152423, -8.196152423}

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