(2w-6)(w)=6400

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Solution for (2w-6)(w)=6400 equation:


Simplifying
(2w + -6)(w) = 6400

Reorder the terms:
(-6 + 2w)(w) = 6400

Reorder the terms for easier multiplication:
w(-6 + 2w) = 6400
(-6 * w + 2w * w) = 6400
(-6w + 2w2) = 6400

Solving
-6w + 2w2 = 6400

Solving for variable 'w'.

Reorder the terms:
-6400 + -6w + 2w2 = 6400 + -6400

Combine like terms: 6400 + -6400 = 0
-6400 + -6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3200 + -3w + w2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3200 + -3w + w2)' equal to zero and attempt to solve: Simplifying -3200 + -3w + w2 = 0 Solving -3200 + -3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '3200' to each side of the equation. -3200 + -3w + 3200 + w2 = 0 + 3200 Reorder the terms: -3200 + 3200 + -3w + w2 = 0 + 3200 Combine like terms: -3200 + 3200 = 0 0 + -3w + w2 = 0 + 3200 -3w + w2 = 0 + 3200 Combine like terms: 0 + 3200 = 3200 -3w + w2 = 3200 The w term is -3w. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3w + 2.25 + w2 = 3200 + 2.25 Reorder the terms: 2.25 + -3w + w2 = 3200 + 2.25 Combine like terms: 3200 + 2.25 = 3202.25 2.25 + -3w + w2 = 3202.25 Factor a perfect square on the left side: (w + -1.5)(w + -1.5) = 3202.25 Calculate the square root of the right side: 56.588426379 Break this problem into two subproblems by setting (w + -1.5) equal to 56.588426379 and -56.588426379.

Subproblem 1

w + -1.5 = 56.588426379 Simplifying w + -1.5 = 56.588426379 Reorder the terms: -1.5 + w = 56.588426379 Solving -1.5 + w = 56.588426379 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = 56.588426379 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = 56.588426379 + 1.5 w = 56.588426379 + 1.5 Combine like terms: 56.588426379 + 1.5 = 58.088426379 w = 58.088426379 Simplifying w = 58.088426379

Subproblem 2

w + -1.5 = -56.588426379 Simplifying w + -1.5 = -56.588426379 Reorder the terms: -1.5 + w = -56.588426379 Solving -1.5 + w = -56.588426379 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = -56.588426379 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = -56.588426379 + 1.5 w = -56.588426379 + 1.5 Combine like terms: -56.588426379 + 1.5 = -55.088426379 w = -55.088426379 Simplifying w = -55.088426379

Solution

The solution to the problem is based on the solutions from the subproblems. w = {58.088426379, -55.088426379}

Solution

w = {58.088426379, -55.088426379}

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