15x^2+35x+19=0

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Solution for 15x^2+35x+19=0 equation:


Simplifying
15x2 + 35x + 19 = 0

Reorder the terms:
19 + 35x + 15x2 = 0

Solving
19 + 35x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
1.266666667 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.266666667' to each side of the equation.
1.266666667 + 2.333333333x + -1.266666667 + x2 = 0 + -1.266666667

Reorder the terms:
1.266666667 + -1.266666667 + 2.333333333x + x2 = 0 + -1.266666667

Combine like terms: 1.266666667 + -1.266666667 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + -1.266666667
2.333333333x + x2 = 0 + -1.266666667

Combine like terms: 0 + -1.266666667 = -1.266666667
2.333333333x + x2 = -1.266666667

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = -1.266666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = -1.266666667 + 1.361111112

Combine like terms: -1.266666667 + 1.361111112 = 0.094444445
1.361111112 + 2.333333333x + x2 = 0.094444445

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 0.094444445

Calculate the square root of the right side: 0.307318149

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 0.307318149 and -0.307318149.

Subproblem 1

x + 1.166666667 = 0.307318149 Simplifying x + 1.166666667 = 0.307318149 Reorder the terms: 1.166666667 + x = 0.307318149 Solving 1.166666667 + x = 0.307318149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 0.307318149 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 0.307318149 + -1.166666667 x = 0.307318149 + -1.166666667 Combine like terms: 0.307318149 + -1.166666667 = -0.859348518 x = -0.859348518 Simplifying x = -0.859348518

Subproblem 2

x + 1.166666667 = -0.307318149 Simplifying x + 1.166666667 = -0.307318149 Reorder the terms: 1.166666667 + x = -0.307318149 Solving 1.166666667 + x = -0.307318149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -0.307318149 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -0.307318149 + -1.166666667 x = -0.307318149 + -1.166666667 Combine like terms: -0.307318149 + -1.166666667 = -1.473984816 x = -1.473984816 Simplifying x = -1.473984816

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.859348518, -1.473984816}

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