(x-7)(3)=(x)(180-x)

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Solution for (x-7)(3)=(x)(180-x) equation:


Simplifying
(x + -7)(3) = (x)(180 + -1x)

Reorder the terms:
(-7 + x)(3) = (x)(180 + -1x)

Reorder the terms for easier multiplication:
3(-7 + x) = (x)(180 + -1x)
(-7 * 3 + x * 3) = (x)(180 + -1x)
(-21 + 3x) = (x)(180 + -1x)
-21 + 3x = (180 * x + -1x * x)
-21 + 3x = (180x + -1x2)

Solving
-21 + 3x = 180x + -1x2

Solving for variable 'x'.

Combine like terms: 3x + -180x = -177x
-21 + -177x + x2 = 180x + -1x2 + -180x + x2

Reorder the terms:
-21 + -177x + x2 = 180x + -180x + -1x2 + x2

Combine like terms: 180x + -180x = 0
-21 + -177x + x2 = 0 + -1x2 + x2
-21 + -177x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-21 + -177x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -177x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + -177x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -177x + x2 = 0 + 21
-177x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
-177x + x2 = 21

The x term is -177x.  Take half its coefficient (-88.5).
Square it (7832.25) and add it to both sides.

Add '7832.25' to each side of the equation.
-177x + 7832.25 + x2 = 21 + 7832.25

Reorder the terms:
7832.25 + -177x + x2 = 21 + 7832.25

Combine like terms: 21 + 7832.25 = 7853.25
7832.25 + -177x + x2 = 7853.25

Factor a perfect square on the left side:
(x + -88.5)(x + -88.5) = 7853.25

Calculate the square root of the right side: 88.618564646

Break this problem into two subproblems by setting 
(x + -88.5) equal to 88.618564646 and -88.618564646.

Subproblem 1

x + -88.5 = 88.618564646 Simplifying x + -88.5 = 88.618564646 Reorder the terms: -88.5 + x = 88.618564646 Solving -88.5 + x = 88.618564646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '88.5' to each side of the equation. -88.5 + 88.5 + x = 88.618564646 + 88.5 Combine like terms: -88.5 + 88.5 = 0.0 0.0 + x = 88.618564646 + 88.5 x = 88.618564646 + 88.5 Combine like terms: 88.618564646 + 88.5 = 177.118564646 x = 177.118564646 Simplifying x = 177.118564646

Subproblem 2

x + -88.5 = -88.618564646 Simplifying x + -88.5 = -88.618564646 Reorder the terms: -88.5 + x = -88.618564646 Solving -88.5 + x = -88.618564646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '88.5' to each side of the equation. -88.5 + 88.5 + x = -88.618564646 + 88.5 Combine like terms: -88.5 + 88.5 = 0.0 0.0 + x = -88.618564646 + 88.5 x = -88.618564646 + 88.5 Combine like terms: -88.618564646 + 88.5 = -0.118564646 x = -0.118564646 Simplifying x = -0.118564646

Solution

The solution to the problem is based on the solutions from the subproblems. x = {177.118564646, -0.118564646}

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