60+0.40x=(12-0.1x)x

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Solution for 60+0.40x=(12-0.1x)x equation:


Simplifying
60 + 0.40x = (12 + -0.1x) * x

Reorder the terms for easier multiplication:
60 + 0.40x = x(12 + -0.1x)
60 + 0.40x = (12 * x + -0.1x * x)
60 + 0.40x = (12x + -0.1x2)

Solving
60 + 0.40x = 12x + -0.1x2

Solving for variable 'x'.

Combine like terms: 0.40x + -12x = -11.6x
60 + -11.6x + 0.1x2 = 12x + -0.1x2 + -12x + 0.1x2

Reorder the terms:
60 + -11.6x + 0.1x2 = 12x + -12x + -0.1x2 + 0.1x2

Combine like terms: 12x + -12x = 0
60 + -11.6x + 0.1x2 = 0 + -0.1x2 + 0.1x2
60 + -11.6x + 0.1x2 = -0.1x2 + 0.1x2

Combine like terms: -0.1x2 + 0.1x2 = 0.0
60 + -11.6x + 0.1x2 = 0.0

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

Divide each side by '0.1'.
600 + -116x + x2 = 0

Move the constant term to the right:

Add '-600' to each side of the equation.
600 + -116x + -600 + x2 = 0 + -600

Reorder the terms:
600 + -600 + -116x + x2 = 0 + -600

Combine like terms: 600 + -600 = 0
0 + -116x + x2 = 0 + -600
-116x + x2 = 0 + -600

Combine like terms: 0 + -600 = -600
-116x + x2 = -600

The x term is -116x.  Take half its coefficient (-58).
Square it (3364) and add it to both sides.

Add '3364' to each side of the equation.
-116x + 3364 + x2 = -600 + 3364

Reorder the terms:
3364 + -116x + x2 = -600 + 3364

Combine like terms: -600 + 3364 = 2764
3364 + -116x + x2 = 2764

Factor a perfect square on the left side:
(x + -58)(x + -58) = 2764

Calculate the square root of the right side: 52.573757712

Break this problem into two subproblems by setting 
(x + -58) equal to 52.573757712 and -52.573757712.

Subproblem 1

x + -58 = 52.573757712 Simplifying x + -58 = 52.573757712 Reorder the terms: -58 + x = 52.573757712 Solving -58 + x = 52.573757712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + x = 52.573757712 + 58 Combine like terms: -58 + 58 = 0 0 + x = 52.573757712 + 58 x = 52.573757712 + 58 Combine like terms: 52.573757712 + 58 = 110.573757712 x = 110.573757712 Simplifying x = 110.573757712

Subproblem 2

x + -58 = -52.573757712 Simplifying x + -58 = -52.573757712 Reorder the terms: -58 + x = -52.573757712 Solving -58 + x = -52.573757712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + x = -52.573757712 + 58 Combine like terms: -58 + 58 = 0 0 + x = -52.573757712 + 58 x = -52.573757712 + 58 Combine like terms: -52.573757712 + 58 = 5.426242288 x = 5.426242288 Simplifying x = 5.426242288

Solution

The solution to the problem is based on the solutions from the subproblems. x = {110.573757712, 5.426242288}

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