5x^2+6x=12

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Solution for 5x^2+6x=12 equation:


Simplifying
5x2 + 6x = 12

Reorder the terms:
6x + 5x2 = 12

Solving
6x + 5x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 6x + 5x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 6x + 5x2 = 0

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

Divide each side by '5'.
-2.4 + 1.2x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 1.2x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 1.2x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 1.2x + x2 = 0 + 2.4
1.2x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
1.2x + x2 = 2.4

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = 2.4 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 2.4 + 0.36

Combine like terms: 2.4 + 0.36 = 2.76
0.36 + 1.2x + x2 = 2.76

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 2.76

Calculate the square root of the right side: 1.661324773

Break this problem into two subproblems by setting 
(x + 0.6) equal to 1.661324773 and -1.661324773.

Subproblem 1

x + 0.6 = 1.661324773 Simplifying x + 0.6 = 1.661324773 Reorder the terms: 0.6 + x = 1.661324773 Solving 0.6 + x = 1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 1.661324773 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.661324773 + -0.6 x = 1.661324773 + -0.6 Combine like terms: 1.661324773 + -0.6 = 1.061324773 x = 1.061324773 Simplifying x = 1.061324773

Subproblem 2

x + 0.6 = -1.661324773 Simplifying x + 0.6 = -1.661324773 Reorder the terms: 0.6 + x = -1.661324773 Solving 0.6 + x = -1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -1.661324773 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.661324773 + -0.6 x = -1.661324773 + -0.6 Combine like terms: -1.661324773 + -0.6 = -2.261324773 x = -2.261324773 Simplifying x = -2.261324773

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.061324773, -2.261324773}

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