-36-2w(w+77)=-4(2w+52)

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Solution for -36-2w(w+77)=-4(2w+52) equation:


Simplifying
-36 + -2w(w + 77) = -4(2w + 52)

Reorder the terms:
-36 + -2w(77 + w) = -4(2w + 52)
-36 + (77 * -2w + w * -2w) = -4(2w + 52)
-36 + (-154w + -2w2) = -4(2w + 52)

Reorder the terms:
-36 + -154w + -2w2 = -4(52 + 2w)
-36 + -154w + -2w2 = (52 * -4 + 2w * -4)
-36 + -154w + -2w2 = (-208 + -8w)

Solving
-36 + -154w + -2w2 = -208 + -8w

Solving for variable 'w'.

Reorder the terms:
-36 + 208 + -154w + 8w + -2w2 = -208 + -8w + 208 + 8w

Combine like terms: -36 + 208 = 172
172 + -154w + 8w + -2w2 = -208 + -8w + 208 + 8w

Combine like terms: -154w + 8w = -146w
172 + -146w + -2w2 = -208 + -8w + 208 + 8w

Reorder the terms:
172 + -146w + -2w2 = -208 + 208 + -8w + 8w

Combine like terms: -208 + 208 = 0
172 + -146w + -2w2 = 0 + -8w + 8w
172 + -146w + -2w2 = -8w + 8w

Combine like terms: -8w + 8w = 0
172 + -146w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(86 + -73w + -1w2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(86 + -73w + -1w2)' equal to zero and attempt to solve: Simplifying 86 + -73w + -1w2 = 0 Solving 86 + -73w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -86 + 73w + w2 = 0 Move the constant term to the right: Add '86' to each side of the equation. -86 + 73w + 86 + w2 = 0 + 86 Reorder the terms: -86 + 86 + 73w + w2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 73w + w2 = 0 + 86 73w + w2 = 0 + 86 Combine like terms: 0 + 86 = 86 73w + w2 = 86 The w term is 73w. Take half its coefficient (36.5). Square it (1332.25) and add it to both sides. Add '1332.25' to each side of the equation. 73w + 1332.25 + w2 = 86 + 1332.25 Reorder the terms: 1332.25 + 73w + w2 = 86 + 1332.25 Combine like terms: 86 + 1332.25 = 1418.25 1332.25 + 73w + w2 = 1418.25 Factor a perfect square on the left side: (w + 36.5)(w + 36.5) = 1418.25 Calculate the square root of the right side: 37.659660115 Break this problem into two subproblems by setting (w + 36.5) equal to 37.659660115 and -37.659660115.

Subproblem 1

w + 36.5 = 37.659660115 Simplifying w + 36.5 = 37.659660115 Reorder the terms: 36.5 + w = 37.659660115 Solving 36.5 + w = 37.659660115 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-36.5' to each side of the equation. 36.5 + -36.5 + w = 37.659660115 + -36.5 Combine like terms: 36.5 + -36.5 = 0.0 0.0 + w = 37.659660115 + -36.5 w = 37.659660115 + -36.5 Combine like terms: 37.659660115 + -36.5 = 1.159660115 w = 1.159660115 Simplifying w = 1.159660115

Subproblem 2

w + 36.5 = -37.659660115 Simplifying w + 36.5 = -37.659660115 Reorder the terms: 36.5 + w = -37.659660115 Solving 36.5 + w = -37.659660115 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-36.5' to each side of the equation. 36.5 + -36.5 + w = -37.659660115 + -36.5 Combine like terms: 36.5 + -36.5 = 0.0 0.0 + w = -37.659660115 + -36.5 w = -37.659660115 + -36.5 Combine like terms: -37.659660115 + -36.5 = -74.159660115 w = -74.159660115 Simplifying w = -74.159660115

Solution

The solution to the problem is based on the solutions from the subproblems. w = {1.159660115, -74.159660115}

Solution

w = {1.159660115, -74.159660115}

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