0=-(239-x)(239-x)+0.012x+0.012x

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Solution for 0=-(239-x)(239-x)+0.012x+0.012x equation:


Simplifying
0 = -1(239 + -1x)(239 + -1x) + 0.012x + 0.012x

Multiply (239 + -1x) * (239 + -1x)
0 = -1(239(239 + -1x) + -1x * (239 + -1x)) + 0.012x + 0.012x
0 = -1((239 * 239 + -1x * 239) + -1x * (239 + -1x)) + 0.012x + 0.012x
0 = -1((57121 + -239x) + -1x * (239 + -1x)) + 0.012x + 0.012x
0 = -1(57121 + -239x + (239 * -1x + -1x * -1x)) + 0.012x + 0.012x
0 = -1(57121 + -239x + (-239x + 1x2)) + 0.012x + 0.012x

Combine like terms: -239x + -239x = -478x
0 = -1(57121 + -478x + 1x2) + 0.012x + 0.012x
0 = (57121 * -1 + -478x * -1 + 1x2 * -1) + 0.012x + 0.012x
0 = (-57121 + 478x + -1x2) + 0.012x + 0.012x

Reorder the terms:
0 = -57121 + 478x + 0.012x + 0.012x + -1x2

Combine like terms: 478x + 0.012x = 478.012x
0 = -57121 + 478.012x + 0.012x + -1x2

Combine like terms: 478.012x + 0.012x = 478.024x
0 = -57121 + 478.024x + -1x2

Solving
0 = -57121 + 478.024x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 57121 = 57121
57121 + -478.024x + x2 = -57121 + 478.024x + -1x2 + 57121 + -478.024x + x2

Reorder the terms:
57121 + -478.024x + x2 = -57121 + 57121 + 478.024x + -478.024x + -1x2 + x2

Combine like terms: -57121 + 57121 = 0
57121 + -478.024x + x2 = 0 + 478.024x + -478.024x + -1x2 + x2
57121 + -478.024x + x2 = 478.024x + -478.024x + -1x2 + x2

Combine like terms: 478.024x + -478.024x = 0.000
57121 + -478.024x + x2 = 0.000 + -1x2 + x2
57121 + -478.024x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
57121 + -478.024x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-57121' to each side of the equation.
57121 + -478.024x + -57121 + x2 = 0 + -57121

Reorder the terms:
57121 + -57121 + -478.024x + x2 = 0 + -57121

Combine like terms: 57121 + -57121 = 0
0 + -478.024x + x2 = 0 + -57121
-478.024x + x2 = 0 + -57121

Combine like terms: 0 + -57121 = -57121
-478.024x + x2 = -57121

The x term is -478.024x.  Take half its coefficient (-239.012).
Square it (57126.73614) and add it to both sides.

Add '57126.73614' to each side of the equation.
-478.024x + 57126.73614 + x2 = -57121 + 57126.73614

Reorder the terms:
57126.73614 + -478.024x + x2 = -57121 + 57126.73614

Combine like terms: -57121 + 57126.73614 = 5.73614
57126.73614 + -478.024x + x2 = 5.73614

Factor a perfect square on the left side:
(x + -239.012)(x + -239.012) = 5.73614

Calculate the square root of the right side: 2.395024008

Break this problem into two subproblems by setting 
(x + -239.012) equal to 2.395024008 and -2.395024008.

Subproblem 1

x + -239.012 = 2.395024008 Simplifying x + -239.012 = 2.395024008 Reorder the terms: -239.012 + x = 2.395024008 Solving -239.012 + x = 2.395024008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '239.012' to each side of the equation. -239.012 + 239.012 + x = 2.395024008 + 239.012 Combine like terms: -239.012 + 239.012 = 0.000 0.000 + x = 2.395024008 + 239.012 x = 2.395024008 + 239.012 Combine like terms: 2.395024008 + 239.012 = 241.407024008 x = 241.407024008 Simplifying x = 241.407024008

Subproblem 2

x + -239.012 = -2.395024008 Simplifying x + -239.012 = -2.395024008 Reorder the terms: -239.012 + x = -2.395024008 Solving -239.012 + x = -2.395024008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '239.012' to each side of the equation. -239.012 + 239.012 + x = -2.395024008 + 239.012 Combine like terms: -239.012 + 239.012 = 0.000 0.000 + x = -2.395024008 + 239.012 x = -2.395024008 + 239.012 Combine like terms: -2.395024008 + 239.012 = 236.616975992 x = 236.616975992 Simplifying x = 236.616975992

Solution

The solution to the problem is based on the solutions from the subproblems. x = {241.407024008, 236.616975992}

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