15x^2+6x-2=0

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Solution for 15x^2+6x-2=0 equation:


Simplifying
15x2 + 6x + -2 = 0

Reorder the terms:
-2 + 6x + 15x2 = 0

Solving
-2 + 6x + 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'.
-0.1333333333 + 0.4x + x2 = 0

Move the constant term to the right:

Add '0.1333333333' to each side of the equation.
-0.1333333333 + 0.4x + 0.1333333333 + x2 = 0 + 0.1333333333

Reorder the terms:
-0.1333333333 + 0.1333333333 + 0.4x + x2 = 0 + 0.1333333333

Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000
0.0000000000 + 0.4x + x2 = 0 + 0.1333333333
0.4x + x2 = 0 + 0.1333333333

Combine like terms: 0 + 0.1333333333 = 0.1333333333
0.4x + x2 = 0.1333333333

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 0.1333333333 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 0.1333333333 + 0.04

Combine like terms: 0.1333333333 + 0.04 = 0.1733333333
0.04 + 0.4x + x2 = 0.1733333333

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.1733333333

Calculate the square root of the right side: 0.4163332

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.4163332 and -0.4163332.

Subproblem 1

x + 0.2 = 0.4163332 Simplifying x + 0.2 = 0.4163332 Reorder the terms: 0.2 + x = 0.4163332 Solving 0.2 + x = 0.4163332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.4163332 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.4163332 + -0.2 x = 0.4163332 + -0.2 Combine like terms: 0.4163332 + -0.2 = 0.2163332 x = 0.2163332 Simplifying x = 0.2163332

Subproblem 2

x + 0.2 = -0.4163332 Simplifying x + 0.2 = -0.4163332 Reorder the terms: 0.2 + x = -0.4163332 Solving 0.2 + x = -0.4163332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.4163332 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.4163332 + -0.2 x = -0.4163332 + -0.2 Combine like terms: -0.4163332 + -0.2 = -0.6163332 x = -0.6163332 Simplifying x = -0.6163332

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2163332, -0.6163332}

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