(18+w)(w)=560

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Solution for (18+w)(w)=560 equation:


Simplifying
(18 + w)(w) = 560

Reorder the terms for easier multiplication:
w(18 + w) = 560
(18 * w + w * w) = 560
(18w + w2) = 560

Solving
18w + w2 = 560

Solving for variable 'w'.

Reorder the terms:
-560 + 18w + w2 = 560 + -560

Combine like terms: 560 + -560 = 0
-560 + 18w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '560' to each side of the equation.
-560 + 18w + 560 + w2 = 0 + 560

Reorder the terms:
-560 + 560 + 18w + w2 = 0 + 560

Combine like terms: -560 + 560 = 0
0 + 18w + w2 = 0 + 560
18w + w2 = 0 + 560

Combine like terms: 0 + 560 = 560
18w + w2 = 560

The w term is 18w.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18w + 81 + w2 = 560 + 81

Reorder the terms:
81 + 18w + w2 = 560 + 81

Combine like terms: 560 + 81 = 641
81 + 18w + w2 = 641

Factor a perfect square on the left side:
(w + 9)(w + 9) = 641

Calculate the square root of the right side: 25.317977802

Break this problem into two subproblems by setting 
(w + 9) equal to 25.317977802 and -25.317977802.

Subproblem 1

w + 9 = 25.317977802 Simplifying w + 9 = 25.317977802 Reorder the terms: 9 + w = 25.317977802 Solving 9 + w = 25.317977802 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = 25.317977802 + -9 Combine like terms: 9 + -9 = 0 0 + w = 25.317977802 + -9 w = 25.317977802 + -9 Combine like terms: 25.317977802 + -9 = 16.317977802 w = 16.317977802 Simplifying w = 16.317977802

Subproblem 2

w + 9 = -25.317977802 Simplifying w + 9 = -25.317977802 Reorder the terms: 9 + w = -25.317977802 Solving 9 + w = -25.317977802 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = -25.317977802 + -9 Combine like terms: 9 + -9 = 0 0 + w = -25.317977802 + -9 w = -25.317977802 + -9 Combine like terms: -25.317977802 + -9 = -34.317977802 w = -34.317977802 Simplifying w = -34.317977802

Solution

The solution to the problem is based on the solutions from the subproblems. w = {16.317977802, -34.317977802}

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