15x^2-35x-28=0

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Solution for 15x^2-35x-28=0 equation: 


Simplifying
15x2 + -35x + -28 = 0

Reorder the terms:
-28 + -35x + 15x2 = 0

Solving
-28 + -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'.
-1.866666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '1.866666667' to each side of the equation.
-1.866666667 + -2.333333333x + 1.866666667 + x2 = 0 + 1.866666667

Reorder the terms:
-1.866666667 + 1.866666667 + -2.333333333x + x2 = 0 + 1.866666667

Combine like terms: -1.866666667 + 1.866666667 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + 1.866666667
-2.333333333x + x2 = 0 + 1.866666667

Combine like terms: 0 + 1.866666667 = 1.866666667
-2.333333333x + x2 = 1.866666667

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 = 1.866666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 1.866666667 + 1.361111112

Combine like terms: 1.866666667 + 1.361111112 = 3.227777779
1.361111112 + -2.333333333x + x2 = 3.227777779

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 3.227777779

Calculate the square root of the right side: 1.796601731

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.796601731 and -1.796601731.


Subproblem 1
x + -1.166666667 = 1.796601731

Simplifying
x + -1.166666667 = 1.796601731

Reorder the terms:
-1.166666667 + x = 1.796601731

Solving
-1.166666667 + x = 1.796601731

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 = 1.796601731 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 1.796601731 + 1.166666667
x = 1.796601731 + 1.166666667

Combine like terms: 1.796601731 + 1.166666667 = 2.963268398
x = 2.963268398

Simplifying
x = 2.963268398


Subproblem 2
x + -1.166666667 = -1.796601731

Simplifying
x + -1.166666667 = -1.796601731

Reorder the terms:
-1.166666667 + x = -1.796601731

Solving
-1.166666667 + x = -1.796601731

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 = -1.796601731 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -1.796601731 + 1.166666667
x = -1.796601731 + 1.166666667

Combine like terms: -1.796601731 + 1.166666667 = -0.629935064
x = -0.629935064

Simplifying
x = -0.629935064


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.963268398, -0.629935064}

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