15x*15x+8x-12=0

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Solution for 15x*15x+8x-12=0 equation:


Simplifying
15x * 15x + 8x + -12 = 0

Reorder the terms for easier multiplication:
15 * 15x * x + 8x + -12 = 0

Multiply 15 * 15
225x * x + 8x + -12 = 0

Multiply x * x
225x2 + 8x + -12 = 0

Reorder the terms:
-12 + 8x + 225x2 = 0

Solving
-12 + 8x + 225x2 = 0

Solving for variable 'x'.

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

Divide each side by '225'.
-0.05333333333 + 0.03555555556x + x2 = 0

Move the constant term to the right:

Add '0.05333333333' to each side of the equation.
-0.05333333333 + 0.03555555556x + 0.05333333333 + x2 = 0 + 0.05333333333

Reorder the terms:
-0.05333333333 + 0.05333333333 + 0.03555555556x + x2 = 0 + 0.05333333333

Combine like terms: -0.05333333333 + 0.05333333333 = 0.00000000000
0.00000000000 + 0.03555555556x + x2 = 0 + 0.05333333333
0.03555555556x + x2 = 0 + 0.05333333333

Combine like terms: 0 + 0.05333333333 = 0.05333333333
0.03555555556x + x2 = 0.05333333333

The x term is 0.03555555556x.  Take half its coefficient (0.01777777778).
Square it (0.0003160493828) and add it to both sides.

Add '0.0003160493828' to each side of the equation.
0.03555555556x + 0.0003160493828 + x2 = 0.05333333333 + 0.0003160493828

Reorder the terms:
0.0003160493828 + 0.03555555556x + x2 = 0.05333333333 + 0.0003160493828

Combine like terms: 0.05333333333 + 0.0003160493828 = 0.0536493827128
0.0003160493828 + 0.03555555556x + x2 = 0.0536493827128

Factor a perfect square on the left side:
(x + 0.01777777778)(x + 0.01777777778) = 0.0536493827128

Calculate the square root of the right side: 0.231623364

Break this problem into two subproblems by setting 
(x + 0.01777777778) equal to 0.231623364 and -0.231623364.

Subproblem 1

x + 0.01777777778 = 0.231623364 Simplifying x + 0.01777777778 = 0.231623364 Reorder the terms: 0.01777777778 + x = 0.231623364 Solving 0.01777777778 + x = 0.231623364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01777777778' to each side of the equation. 0.01777777778 + -0.01777777778 + x = 0.231623364 + -0.01777777778 Combine like terms: 0.01777777778 + -0.01777777778 = 0.00000000000 0.00000000000 + x = 0.231623364 + -0.01777777778 x = 0.231623364 + -0.01777777778 Combine like terms: 0.231623364 + -0.01777777778 = 0.21384558622 x = 0.21384558622 Simplifying x = 0.21384558622

Subproblem 2

x + 0.01777777778 = -0.231623364 Simplifying x + 0.01777777778 = -0.231623364 Reorder the terms: 0.01777777778 + x = -0.231623364 Solving 0.01777777778 + x = -0.231623364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01777777778' to each side of the equation. 0.01777777778 + -0.01777777778 + x = -0.231623364 + -0.01777777778 Combine like terms: 0.01777777778 + -0.01777777778 = 0.00000000000 0.00000000000 + x = -0.231623364 + -0.01777777778 x = -0.231623364 + -0.01777777778 Combine like terms: -0.231623364 + -0.01777777778 = -0.24940114178 x = -0.24940114178 Simplifying x = -0.24940114178

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.21384558622, -0.24940114178}

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