-15x^2+35x-8=0

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Solution for -15x^2+35x-8=0 equation: 


Simplifying
-15x2 + 35x + -8 = 0

Reorder the terms:
-8 + 35x + -15x2 = 0

Solving
-8 + 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'.
0.5333333333 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '-0.5333333333' to each side of the equation.
0.5333333333 + -2.333333333x + -0.5333333333 + x2 = 0 + -0.5333333333

Reorder the terms:
0.5333333333 + -0.5333333333 + -2.333333333x + x2 = 0 + -0.5333333333

Combine like terms: 0.5333333333 + -0.5333333333 = 0.0000000000
0.0000000000 + -2.333333333x + x2 = 0 + -0.5333333333
-2.333333333x + x2 = 0 + -0.5333333333

Combine like terms: 0 + -0.5333333333 = -0.5333333333
-2.333333333x + x2 = -0.5333333333

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 = -0.5333333333 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = -0.5333333333 + 1.361111112

Combine like terms: -0.5333333333 + 1.361111112 = 0.8277777787
1.361111112 + -2.333333333x + x2 = 0.8277777787

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 0.8277777787

Calculate the square root of the right side: 0.909822938

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 0.909822938 and -0.909822938.


Subproblem 1
x + -1.166666667 = 0.909822938

Simplifying
x + -1.166666667 = 0.909822938

Reorder the terms:
-1.166666667 + x = 0.909822938

Solving
-1.166666667 + x = 0.909822938

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 = 0.909822938 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 0.909822938 + 1.166666667
x = 0.909822938 + 1.166666667

Combine like terms: 0.909822938 + 1.166666667 = 2.076489605
x = 2.076489605

Simplifying
x = 2.076489605


Subproblem 2
x + -1.166666667 = -0.909822938

Simplifying
x + -1.166666667 = -0.909822938

Reorder the terms:
-1.166666667 + x = -0.909822938

Solving
-1.166666667 + x = -0.909822938

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 = -0.909822938 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -0.909822938 + 1.166666667
x = -0.909822938 + 1.166666667

Combine like terms: -0.909822938 + 1.166666667 = 0.256843729
x = 0.256843729

Simplifying
x = 0.256843729


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.076489605, 0.256843729}

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