(5+w)(w-2)=162

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Solution for (5+w)(w-2)=162 equation:


Simplifying
(5 + w)(w + -2) = 162

Reorder the terms:
(5 + w)(-2 + w) = 162

Multiply (5 + w) * (-2 + w)
(5(-2 + w) + w(-2 + w)) = 162
((-2 * 5 + w * 5) + w(-2 + w)) = 162
((-10 + 5w) + w(-2 + w)) = 162
(-10 + 5w + (-2 * w + w * w)) = 162
(-10 + 5w + (-2w + w2)) = 162

Combine like terms: 5w + -2w = 3w
(-10 + 3w + w2) = 162

Solving
-10 + 3w + w2 = 162

Solving for variable 'w'.

Reorder the terms:
-10 + -162 + 3w + w2 = 162 + -162

Combine like terms: -10 + -162 = -172
-172 + 3w + w2 = 162 + -162

Combine like terms: 162 + -162 = 0
-172 + 3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '172' to each side of the equation.
-172 + 3w + 172 + w2 = 0 + 172

Reorder the terms:
-172 + 172 + 3w + w2 = 0 + 172

Combine like terms: -172 + 172 = 0
0 + 3w + w2 = 0 + 172
3w + w2 = 0 + 172

Combine like terms: 0 + 172 = 172
3w + w2 = 172

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 = 172 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 172 + 2.25

Combine like terms: 172 + 2.25 = 174.25
2.25 + 3w + w2 = 174.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 174.25

Calculate the square root of the right side: 13.200378782

Break this problem into two subproblems by setting 
(w + 1.5) equal to 13.200378782 and -13.200378782.

Subproblem 1

w + 1.5 = 13.200378782 Simplifying w + 1.5 = 13.200378782 Reorder the terms: 1.5 + w = 13.200378782 Solving 1.5 + w = 13.200378782 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 = 13.200378782 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 13.200378782 + -1.5 w = 13.200378782 + -1.5 Combine like terms: 13.200378782 + -1.5 = 11.700378782 w = 11.700378782 Simplifying w = 11.700378782

Subproblem 2

w + 1.5 = -13.200378782 Simplifying w + 1.5 = -13.200378782 Reorder the terms: 1.5 + w = -13.200378782 Solving 1.5 + w = -13.200378782 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 = -13.200378782 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -13.200378782 + -1.5 w = -13.200378782 + -1.5 Combine like terms: -13.200378782 + -1.5 = -14.700378782 w = -14.700378782 Simplifying w = -14.700378782

Solution

The solution to the problem is based on the solutions from the subproblems. w = {11.700378782, -14.700378782}

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