15x^2+8x=3

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Solution for 15x^2+8x=3 equation:


Simplifying
15x2 + 8x = 3

Reorder the terms:
8x + 15x2 = 3

Solving
8x + 15x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 8x + 15x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 8x + 15x2 = 0

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

Divide each side by '15'.
-0.2 + 0.5333333333x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.5333333333x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.5333333333x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.5333333333x + x2 = 0 + 0.2
0.5333333333x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
0.5333333333x + x2 = 0.2

The x term is 0.5333333333x.  Take half its coefficient (0.2666666667).
Square it (0.07111111113) and add it to both sides.

Add '0.07111111113' to each side of the equation.
0.5333333333x + 0.07111111113 + x2 = 0.2 + 0.07111111113

Reorder the terms:
0.07111111113 + 0.5333333333x + x2 = 0.2 + 0.07111111113

Combine like terms: 0.2 + 0.07111111113 = 0.27111111113
0.07111111113 + 0.5333333333x + x2 = 0.27111111113

Factor a perfect square on the left side:
(x + 0.2666666667)(x + 0.2666666667) = 0.27111111113

Calculate the square root of the right side: 0.520683312

Break this problem into two subproblems by setting 
(x + 0.2666666667) equal to 0.520683312 and -0.520683312.

Subproblem 1

x + 0.2666666667 = 0.520683312 Simplifying x + 0.2666666667 = 0.520683312 Reorder the terms: 0.2666666667 + x = 0.520683312 Solving 0.2666666667 + x = 0.520683312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2666666667' to each side of the equation. 0.2666666667 + -0.2666666667 + x = 0.520683312 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + x = 0.520683312 + -0.2666666667 x = 0.520683312 + -0.2666666667 Combine like terms: 0.520683312 + -0.2666666667 = 0.2540166453 x = 0.2540166453 Simplifying x = 0.2540166453

Subproblem 2

x + 0.2666666667 = -0.520683312 Simplifying x + 0.2666666667 = -0.520683312 Reorder the terms: 0.2666666667 + x = -0.520683312 Solving 0.2666666667 + x = -0.520683312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2666666667' to each side of the equation. 0.2666666667 + -0.2666666667 + x = -0.520683312 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + x = -0.520683312 + -0.2666666667 x = -0.520683312 + -0.2666666667 Combine like terms: -0.520683312 + -0.2666666667 = -0.7873499787 x = -0.7873499787 Simplifying x = -0.7873499787

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2540166453, -0.7873499787}

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