-2x^2+13x=12

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Solution for -2x^2+13x=12 equation:


Simplifying
-2x2 + 13x = 12

Reorder the terms:
13x + -2x2 = 12

Solving
13x + -2x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 13x + -2x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 13x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
6 + -6.5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -6.5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -6.5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -6.5x + x2 = 0 + -6
-6.5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-6.5x + x2 = -6

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = -6 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -6 + 10.5625

Combine like terms: -6 + 10.5625 = 4.5625
10.5625 + -6.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + -3.25) equal to 2.136000936 and -2.136000936.

Subproblem 1

x + -3.25 = 2.136000936 Simplifying x + -3.25 = 2.136000936 Reorder the terms: -3.25 + x = 2.136000936 Solving -3.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 2.136000936 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.136000936 + 3.25 x = 2.136000936 + 3.25 Combine like terms: 2.136000936 + 3.25 = 5.386000936 x = 5.386000936 Simplifying x = 5.386000936

Subproblem 2

x + -3.25 = -2.136000936 Simplifying x + -3.25 = -2.136000936 Reorder the terms: -3.25 + x = -2.136000936 Solving -3.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -2.136000936 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.136000936 + 3.25 x = -2.136000936 + 3.25 Combine like terms: -2.136000936 + 3.25 = 1.113999064 x = 1.113999064 Simplifying x = 1.113999064

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.386000936, 1.113999064}

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