15x^2-28x+7=0

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Solution for 15x^2-28x+7=0 equation: 


Simplifying
15x2 + -28x + 7 = 0

Reorder the terms:
7 + -28x + 15x2 = 0

Solving
7 + -28x + 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'.
0.4666666667 + -1.866666667x + x2 = 0

Move the constant term to the right:

Add '-0.4666666667' to each side of the equation.
0.4666666667 + -1.866666667x + -0.4666666667 + x2 = 0 + -0.4666666667

Reorder the terms:
0.4666666667 + -0.4666666667 + -1.866666667x + x2 = 0 + -0.4666666667

Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000
0.0000000000 + -1.866666667x + x2 = 0 + -0.4666666667
-1.866666667x + x2 = 0 + -0.4666666667

Combine like terms: 0 + -0.4666666667 = -0.4666666667
-1.866666667x + x2 = -0.4666666667

The x term is -1.866666667x.  Take half its coefficient (-0.9333333335).
Square it (0.8711111114) and add it to both sides.

Add '0.8711111114' to each side of the equation.
-1.866666667x + 0.8711111114 + x2 = -0.4666666667 + 0.8711111114

Reorder the terms:
0.8711111114 + -1.866666667x + x2 = -0.4666666667 + 0.8711111114

Combine like terms: -0.4666666667 + 0.8711111114 = 0.4044444447
0.8711111114 + -1.866666667x + x2 = 0.4044444447

Factor a perfect square on the left side:
(x + -0.9333333335)(x + -0.9333333335) = 0.4044444447

Calculate the square root of the right side: 0.635959468

Break this problem into two subproblems by setting 
(x + -0.9333333335) equal to 0.635959468 and -0.635959468.


Subproblem 1
x + -0.9333333335 = 0.635959468

Simplifying
x + -0.9333333335 = 0.635959468

Reorder the terms:
-0.9333333335 + x = 0.635959468

Solving
-0.9333333335 + x = 0.635959468

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.9333333335' to each side of the equation.
-0.9333333335 + 0.9333333335 + x = 0.635959468 + 0.9333333335

Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000
0.0000000000 + x = 0.635959468 + 0.9333333335
x = 0.635959468 + 0.9333333335

Combine like terms: 0.635959468 + 0.9333333335 = 1.5692928015
x = 1.5692928015

Simplifying
x = 1.5692928015


Subproblem 2
x + -0.9333333335 = -0.635959468

Simplifying
x + -0.9333333335 = -0.635959468

Reorder the terms:
-0.9333333335 + x = -0.635959468

Solving
-0.9333333335 + x = -0.635959468

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.9333333335' to each side of the equation.
-0.9333333335 + 0.9333333335 + x = -0.635959468 + 0.9333333335

Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000
0.0000000000 + x = -0.635959468 + 0.9333333335
x = -0.635959468 + 0.9333333335

Combine like terms: -0.635959468 + 0.9333333335 = 0.2973738655
x = 0.2973738655

Simplifying
x = 0.2973738655


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5692928015, 0.2973738655}

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