140.24=x^2+4x

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Solution for 140.24=x^2+4x equation:


Simplifying
140.24 = x2 + 4x

Reorder the terms:
140.24 = 4x + x2

Solving
140.24 = 4x + x2

Solving for variable 'x'.

Reorder the terms:
140.24 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
140.24 + -4x + -1x2 = 0 + x2 + -1x2
140.24 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
140.24 + -4x + -1x2 = 0

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

Divide each side by '-1'.
-140.24 + 4x + x2 = 0

Move the constant term to the right:

Add '140.24' to each side of the equation.
-140.24 + 4x + 140.24 + x2 = 0 + 140.24

Reorder the terms:
-140.24 + 140.24 + 4x + x2 = 0 + 140.24

Combine like terms: -140.24 + 140.24 = 0.00
0.00 + 4x + x2 = 0 + 140.24
4x + x2 = 0 + 140.24

Combine like terms: 0 + 140.24 = 140.24
4x + x2 = 140.24

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 140.24 + 4

Reorder the terms:
4 + 4x + x2 = 140.24 + 4

Combine like terms: 140.24 + 4 = 144.24
4 + 4x + x2 = 144.24

Factor a perfect square on the left side:
(x + 2)(x + 2) = 144.24

Calculate the square root of the right side: 12.009995837

Break this problem into two subproblems by setting 
(x + 2) equal to 12.009995837 and -12.009995837.

Subproblem 1

x + 2 = 12.009995837 Simplifying x + 2 = 12.009995837 Reorder the terms: 2 + x = 12.009995837 Solving 2 + x = 12.009995837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 12.009995837 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.009995837 + -2 x = 12.009995837 + -2 Combine like terms: 12.009995837 + -2 = 10.009995837 x = 10.009995837 Simplifying x = 10.009995837

Subproblem 2

x + 2 = -12.009995837 Simplifying x + 2 = -12.009995837 Reorder the terms: 2 + x = -12.009995837 Solving 2 + x = -12.009995837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -12.009995837 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.009995837 + -2 x = -12.009995837 + -2 Combine like terms: -12.009995837 + -2 = -14.009995837 x = -14.009995837 Simplifying x = -14.009995837

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.009995837, -14.009995837}

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