3w^2-36w+36=

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Solution for 3w^2-36w+36= equation:


Simplifying
3w2 + -36w + 36 = 0

Reorder the terms:
36 + -36w + 3w2 = 0

Solving
36 + -36w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -12w + w2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(12 + -12w + w2)' equal to zero and attempt to solve: Simplifying 12 + -12w + w2 = 0 Solving 12 + -12w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -12w + -12 + w2 = 0 + -12 Reorder the terms: 12 + -12 + -12w + w2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -12w + w2 = 0 + -12 -12w + w2 = 0 + -12 Combine like terms: 0 + -12 = -12 -12w + w2 = -12 The w term is -12w. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12w + 36 + w2 = -12 + 36 Reorder the terms: 36 + -12w + w2 = -12 + 36 Combine like terms: -12 + 36 = 24 36 + -12w + w2 = 24 Factor a perfect square on the left side: (w + -6)(w + -6) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (w + -6) equal to 4.898979486 and -4.898979486.

Subproblem 1

w + -6 = 4.898979486 Simplifying w + -6 = 4.898979486 Reorder the terms: -6 + w = 4.898979486 Solving -6 + w = 4.898979486 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = 4.898979486 + 6 Combine like terms: -6 + 6 = 0 0 + w = 4.898979486 + 6 w = 4.898979486 + 6 Combine like terms: 4.898979486 + 6 = 10.898979486 w = 10.898979486 Simplifying w = 10.898979486

Subproblem 2

w + -6 = -4.898979486 Simplifying w + -6 = -4.898979486 Reorder the terms: -6 + w = -4.898979486 Solving -6 + w = -4.898979486 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = -4.898979486 + 6 Combine like terms: -6 + 6 = 0 0 + w = -4.898979486 + 6 w = -4.898979486 + 6 Combine like terms: -4.898979486 + 6 = 1.101020514 w = 1.101020514 Simplifying w = 1.101020514

Solution

The solution to the problem is based on the solutions from the subproblems. w = {10.898979486, 1.101020514}

Solution

w = {10.898979486, 1.101020514}

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