x^2=16x^2-15x+10

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Solution for x^2=16x^2-15x+10 equation: 


Simplifying
x2 = 16x2 + -15x + 10

Reorder the terms:
x2 = 10 + -15x + 16x2

Solving
x2 = 10 + -15x + 16x2

Solving for variable 'x'.

Reorder the terms:
-10 + 15x + x2 + -16x2 = 10 + -15x + 16x2 + -10 + 15x + -16x2

Combine like terms: x2 + -16x2 = -15x2
-10 + 15x + -15x2 = 10 + -15x + 16x2 + -10 + 15x + -16x2

Reorder the terms:
-10 + 15x + -15x2 = 10 + -10 + -15x + 15x + 16x2 + -16x2

Combine like terms: 10 + -10 = 0
-10 + 15x + -15x2 = 0 + -15x + 15x + 16x2 + -16x2
-10 + 15x + -15x2 = -15x + 15x + 16x2 + -16x2

Combine like terms: -15x + 15x = 0
-10 + 15x + -15x2 = 0 + 16x2 + -16x2
-10 + 15x + -15x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-10 + 15x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 3x + -3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + 3x + -3x2)' equal to zero and attempt to solve:

Simplifying
-2 + 3x + -3x2 = 0

Solving
-2 + 3x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
0.6666666667 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -1x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -1x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + -0.6666666667
-1x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-1x + x2 = -0.6666666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.6666666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.6666666667 + 0.25

Combine like terms: -0.6666666667 + 0.25 = -0.4166666667
0.25 + -1x + x2 = -0.4166666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -0.4166666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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