5x^2+12x+1=0

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Solution for 5x^2+12x+1=0 equation:


Simplifying
5x2 + 12x + 1 = 0

Reorder the terms:
1 + 12x + 5x2 = 0

Solving
1 + 12x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
0.2 + 2.4x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 2.4x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 2.4x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 2.4x + x2 = 0 + -0.2
2.4x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
2.4x + x2 = -0.2

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 = -0.2 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = -0.2 + 1.44

Combine like terms: -0.2 + 1.44 = 1.24
1.44 + 2.4x + x2 = 1.24

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(x + 1.2) equal to 1.113552873 and -1.113552873.

Subproblem 1

x + 1.2 = 1.113552873 Simplifying x + 1.2 = 1.113552873 Reorder the terms: 1.2 + x = 1.113552873 Solving 1.2 + x = 1.113552873 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 = 1.113552873 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.113552873 + -1.2 x = 1.113552873 + -1.2 Combine like terms: 1.113552873 + -1.2 = -0.086447127 x = -0.086447127 Simplifying x = -0.086447127

Subproblem 2

x + 1.2 = -1.113552873 Simplifying x + 1.2 = -1.113552873 Reorder the terms: 1.2 + x = -1.113552873 Solving 1.2 + x = -1.113552873 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 = -1.113552873 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.113552873 + -1.2 x = -1.113552873 + -1.2 Combine like terms: -1.113552873 + -1.2 = -2.313552873 x = -2.313552873 Simplifying x = -2.313552873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.086447127, -2.313552873}

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