10x+140=2x+x^2

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Solution for 10x+140=2x+x^2 equation:


Simplifying
10x + 140 = 2x + x2

Reorder the terms:
140 + 10x = 2x + x2

Solving
140 + 10x = 2x + x2

Solving for variable 'x'.

Combine like terms: 10x + -2x = 8x
140 + 8x + -1x2 = 2x + x2 + -2x + -1x2

Reorder the terms:
140 + 8x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
140 + 8x + -1x2 = 0 + x2 + -1x2
140 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
140 + 8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-140 + -8x + x2 = 0

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + -8x + 140 + x2 = 0 + 140

Reorder the terms:
-140 + 140 + -8x + x2 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + -8x + x2 = 0 + 140
-8x + x2 = 0 + 140

Combine like terms: 0 + 140 = 140
-8x + x2 = 140

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 140 + 16

Reorder the terms:
16 + -8x + x2 = 140 + 16

Combine like terms: 140 + 16 = 156
16 + -8x + x2 = 156

Factor a perfect square on the left side:
(x + -4)(x + -4) = 156

Calculate the square root of the right side: 12.489995997

Break this problem into two subproblems by setting 
(x + -4) equal to 12.489995997 and -12.489995997.

Subproblem 1

x + -4 = 12.489995997 Simplifying x + -4 = 12.489995997 Reorder the terms: -4 + x = 12.489995997 Solving -4 + x = 12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 12.489995997 + 4 Combine like terms: -4 + 4 = 0 0 + x = 12.489995997 + 4 x = 12.489995997 + 4 Combine like terms: 12.489995997 + 4 = 16.489995997 x = 16.489995997 Simplifying x = 16.489995997

Subproblem 2

x + -4 = -12.489995997 Simplifying x + -4 = -12.489995997 Reorder the terms: -4 + x = -12.489995997 Solving -4 + x = -12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -12.489995997 + 4 Combine like terms: -4 + 4 = 0 0 + x = -12.489995997 + 4 x = -12.489995997 + 4 Combine like terms: -12.489995997 + 4 = -8.489995997 x = -8.489995997 Simplifying x = -8.489995997

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.489995997, -8.489995997}

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