10x+(12-x)=10x(12-x)+x+54

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Solution for 10x+(12-x)=10x(12-x)+x+54 equation:


Simplifying
10x + (12 + -1x) = 10x(12 + -1x) + x + 54

Remove parenthesis around (12 + -1x)
10x + 12 + -1x = 10x(12 + -1x) + x + 54

Reorder the terms:
12 + 10x + -1x = 10x(12 + -1x) + x + 54

Combine like terms: 10x + -1x = 9x
12 + 9x = 10x(12 + -1x) + x + 54
12 + 9x = (12 * 10x + -1x * 10x) + x + 54
12 + 9x = (120x + -10x2) + x + 54

Reorder the terms:
12 + 9x = 54 + 120x + x + -10x2

Combine like terms: 120x + x = 121x
12 + 9x = 54 + 121x + -10x2

Solving
12 + 9x = 54 + 121x + -10x2

Solving for variable 'x'.

Reorder the terms:
12 + -54 + 9x + -121x + 10x2 = 54 + 121x + -10x2 + -54 + -121x + 10x2

Combine like terms: 12 + -54 = -42
-42 + 9x + -121x + 10x2 = 54 + 121x + -10x2 + -54 + -121x + 10x2

Combine like terms: 9x + -121x = -112x
-42 + -112x + 10x2 = 54 + 121x + -10x2 + -54 + -121x + 10x2

Reorder the terms:
-42 + -112x + 10x2 = 54 + -54 + 121x + -121x + -10x2 + 10x2

Combine like terms: 54 + -54 = 0
-42 + -112x + 10x2 = 0 + 121x + -121x + -10x2 + 10x2
-42 + -112x + 10x2 = 121x + -121x + -10x2 + 10x2

Combine like terms: 121x + -121x = 0
-42 + -112x + 10x2 = 0 + -10x2 + 10x2
-42 + -112x + 10x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
-42 + -112x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -56x + 5x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-21 + -56x + 5x2)' equal to zero and attempt to solve: Simplifying -21 + -56x + 5x2 = 0 Solving -21 + -56x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + -11.2x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -11.2x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -11.2x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -11.2x + x2 = 0 + 4.2 -11.2x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -11.2x + x2 = 4.2 The x term is -11.2x. Take half its coefficient (-5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. -11.2x + 31.36 + x2 = 4.2 + 31.36 Reorder the terms: 31.36 + -11.2x + x2 = 4.2 + 31.36 Combine like terms: 4.2 + 31.36 = 35.56 31.36 + -11.2x + x2 = 35.56 Factor a perfect square on the left side: (x + -5.6)(x + -5.6) = 35.56 Calculate the square root of the right side: 5.963220606 Break this problem into two subproblems by setting (x + -5.6) equal to 5.963220606 and -5.963220606.

Subproblem 1

x + -5.6 = 5.963220606 Simplifying x + -5.6 = 5.963220606 Reorder the terms: -5.6 + x = 5.963220606 Solving -5.6 + x = 5.963220606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + x = 5.963220606 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = 5.963220606 + 5.6 x = 5.963220606 + 5.6 Combine like terms: 5.963220606 + 5.6 = 11.563220606 x = 11.563220606 Simplifying x = 11.563220606

Subproblem 2

x + -5.6 = -5.963220606 Simplifying x + -5.6 = -5.963220606 Reorder the terms: -5.6 + x = -5.963220606 Solving -5.6 + x = -5.963220606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + x = -5.963220606 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = -5.963220606 + 5.6 x = -5.963220606 + 5.6 Combine like terms: -5.963220606 + 5.6 = -0.363220606 x = -0.363220606 Simplifying x = -0.363220606

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.563220606, -0.363220606}

Solution

x = {11.563220606, -0.363220606}

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