1.3x^2+6x+4=0

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Solution for 1.3x^2+6x+4=0 equation:


Simplifying
1.3x2 + 6x + 4 = 0

Reorder the terms:
4 + 6x + 1.3x2 = 0

Solving
4 + 6x + 1.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.3'.
3.076923077 + 4.615384615x + x2 = 0

Move the constant term to the right:

Add '-3.076923077' to each side of the equation.
3.076923077 + 4.615384615x + -3.076923077 + x2 = 0 + -3.076923077

Reorder the terms:
3.076923077 + -3.076923077 + 4.615384615x + x2 = 0 + -3.076923077

Combine like terms: 3.076923077 + -3.076923077 = 0.000000000
0.000000000 + 4.615384615x + x2 = 0 + -3.076923077
4.615384615x + x2 = 0 + -3.076923077

Combine like terms: 0 + -3.076923077 = -3.076923077
4.615384615x + x2 = -3.076923077

The x term is 4.615384615x.  Take half its coefficient (2.307692308).
Square it (5.325443788) and add it to both sides.

Add '5.325443788' to each side of the equation.
4.615384615x + 5.325443788 + x2 = -3.076923077 + 5.325443788

Reorder the terms:
5.325443788 + 4.615384615x + x2 = -3.076923077 + 5.325443788

Combine like terms: -3.076923077 + 5.325443788 = 2.248520711
5.325443788 + 4.615384615x + x2 = 2.248520711

Factor a perfect square on the left side:
(x + 2.307692308)(x + 2.307692308) = 2.248520711

Calculate the square root of the right side: 1.499506823

Break this problem into two subproblems by setting 
(x + 2.307692308) equal to 1.499506823 and -1.499506823.

Subproblem 1

x + 2.307692308 = 1.499506823 Simplifying x + 2.307692308 = 1.499506823 Reorder the terms: 2.307692308 + x = 1.499506823 Solving 2.307692308 + x = 1.499506823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.307692308' to each side of the equation. 2.307692308 + -2.307692308 + x = 1.499506823 + -2.307692308 Combine like terms: 2.307692308 + -2.307692308 = 0.000000000 0.000000000 + x = 1.499506823 + -2.307692308 x = 1.499506823 + -2.307692308 Combine like terms: 1.499506823 + -2.307692308 = -0.808185485 x = -0.808185485 Simplifying x = -0.808185485

Subproblem 2

x + 2.307692308 = -1.499506823 Simplifying x + 2.307692308 = -1.499506823 Reorder the terms: 2.307692308 + x = -1.499506823 Solving 2.307692308 + x = -1.499506823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.307692308' to each side of the equation. 2.307692308 + -2.307692308 + x = -1.499506823 + -2.307692308 Combine like terms: 2.307692308 + -2.307692308 = 0.000000000 0.000000000 + x = -1.499506823 + -2.307692308 x = -1.499506823 + -2.307692308 Combine like terms: -1.499506823 + -2.307692308 = -3.807199131 x = -3.807199131 Simplifying x = -3.807199131

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.808185485, -3.807199131}

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