5x^2+12x=2

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


Simplifying
5x2 + 12x = 2

Reorder the terms:
12x + 5x2 = 2

Solving
12x + 5x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 12x + 5x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 12x + 5x2 = 0

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

Divide each side by '5'.
-0.4 + 2.4x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 2.4x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 2.4x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 2.4x + x2 = 0 + 0.4
2.4x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
2.4x + x2 = 0.4

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = 0.4 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 0.4 + 1.44

Combine like terms: 0.4 + 1.44 = 1.84
1.44 + 2.4x + x2 = 1.84

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 1.84

Calculate the square root of the right side: 1.356465997

Break this problem into two subproblems by setting 
(x + 1.2) equal to 1.356465997 and -1.356465997.

Subproblem 1

x + 1.2 = 1.356465997 Simplifying x + 1.2 = 1.356465997 Reorder the terms: 1.2 + x = 1.356465997 Solving 1.2 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.356465997 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.356465997 + -1.2 x = 1.356465997 + -1.2 Combine like terms: 1.356465997 + -1.2 = 0.156465997 x = 0.156465997 Simplifying x = 0.156465997

Subproblem 2

x + 1.2 = -1.356465997 Simplifying x + 1.2 = -1.356465997 Reorder the terms: 1.2 + x = -1.356465997 Solving 1.2 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.356465997 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.356465997 + -1.2 x = -1.356465997 + -1.2 Combine like terms: -1.356465997 + -1.2 = -2.556465997 x = -2.556465997 Simplifying x = -2.556465997

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.156465997, -2.556465997}

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