5x^2+18x+1=0

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Solution for 5x^2+18x+1=0 equation:


Simplifying
5x2 + 18x + 1 = 0

Reorder the terms:
1 + 18x + 5x2 = 0

Solving
1 + 18x + 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 + 3.6x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 3.6x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 3.6x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 3.6x + x2 = 0 + -0.2
3.6x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
3.6x + x2 = -0.2

The x term is 3.6x.  Take half its coefficient (1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
3.6x + 3.24 + x2 = -0.2 + 3.24

Reorder the terms:
3.24 + 3.6x + x2 = -0.2 + 3.24

Combine like terms: -0.2 + 3.24 = 3.04
3.24 + 3.6x + x2 = 3.04

Factor a perfect square on the left side:
(x + 1.8)(x + 1.8) = 3.04

Calculate the square root of the right side: 1.743559577

Break this problem into two subproblems by setting 
(x + 1.8) equal to 1.743559577 and -1.743559577.

Subproblem 1

x + 1.8 = 1.743559577 Simplifying x + 1.8 = 1.743559577 Reorder the terms: 1.8 + x = 1.743559577 Solving 1.8 + x = 1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 1.743559577 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 1.743559577 + -1.8 x = 1.743559577 + -1.8 Combine like terms: 1.743559577 + -1.8 = -0.056440423 x = -0.056440423 Simplifying x = -0.056440423

Subproblem 2

x + 1.8 = -1.743559577 Simplifying x + 1.8 = -1.743559577 Reorder the terms: 1.8 + x = -1.743559577 Solving 1.8 + x = -1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -1.743559577 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -1.743559577 + -1.8 x = -1.743559577 + -1.8 Combine like terms: -1.743559577 + -1.8 = -3.543559577 x = -3.543559577 Simplifying x = -3.543559577

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.056440423, -3.543559577}

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