12x^2=-10x+5

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Solution for 12x^2=-10x+5 equation:


Simplifying
12x2 = -10x + 5

Reorder the terms:
12x2 = 5 + -10x

Solving
12x2 = 5 + -10x

Solving for variable 'x'.

Reorder the terms:
-5 + 10x + 12x2 = 5 + -10x + -5 + 10x

Reorder the terms:
-5 + 10x + 12x2 = 5 + -5 + -10x + 10x

Combine like terms: 5 + -5 = 0
-5 + 10x + 12x2 = 0 + -10x + 10x
-5 + 10x + 12x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
-5 + 10x + 12x2 = 0

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

Divide each side by '12'.
-0.4166666667 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.8333333333x + 0.4166666667 + x2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + 0.8333333333x + x2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + 0.8333333333x + x2 = 0 + 0.4166666667
0.8333333333x + x2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
0.8333333333x + x2 = 0.4166666667

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = 0.4166666667 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = 0.4166666667 + 0.1736111111

Combine like terms: 0.4166666667 + 0.1736111111 = 0.5902777778
0.1736111111 + 0.8333333333x + x2 = 0.5902777778

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = 0.5902777778

Calculate the square root of the right side: 0.768295371

Break this problem into two subproblems by setting 
(x + 0.4166666667) equal to 0.768295371 and -0.768295371.

Subproblem 1

x + 0.4166666667 = 0.768295371 Simplifying x + 0.4166666667 = 0.768295371 Reorder the terms: 0.4166666667 + x = 0.768295371 Solving 0.4166666667 + x = 0.768295371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 0.768295371 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 0.768295371 + -0.4166666667 x = 0.768295371 + -0.4166666667 Combine like terms: 0.768295371 + -0.4166666667 = 0.3516287043 x = 0.3516287043 Simplifying x = 0.3516287043

Subproblem 2

x + 0.4166666667 = -0.768295371 Simplifying x + 0.4166666667 = -0.768295371 Reorder the terms: 0.4166666667 + x = -0.768295371 Solving 0.4166666667 + x = -0.768295371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -0.768295371 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -0.768295371 + -0.4166666667 x = -0.768295371 + -0.4166666667 Combine like terms: -0.768295371 + -0.4166666667 = -1.1849620377 x = -1.1849620377 Simplifying x = -1.1849620377

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3516287043, -1.1849620377}

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