13x(13x)+9x-4-7x(7x)+15x-6=

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Solution for 13x(13x)+9x-4-7x(7x)+15x-6= equation: 


Simplifying
13x(13x) + 9x + -4 + -7x(7x) + 15x + -6 = 0

Remove parenthesis around (13x)
13x * 13x + 9x + -4 + -7x(7x) + 15x + -6 = 0

Reorder the terms for easier multiplication:
13 * 13x * x + 9x + -4 + -7x(7x) + 15x + -6 = 0

Multiply 13 * 13
169x * x + 9x + -4 + -7x(7x) + 15x + -6 = 0

Multiply x * x
169x2 + 9x + -4 + -7x(7x) + 15x + -6 = 0

Remove parenthesis around (7x)
169x2 + 9x + -4 + -7x * 7x + 15x + -6 = 0

Reorder the terms for easier multiplication:
169x2 + 9x + -4 + -7 * 7x * x + 15x + -6 = 0

Multiply -7 * 7
169x2 + 9x + -4 + -49x * x + 15x + -6 = 0

Multiply x * x
169x2 + 9x + -4 + -49x2 + 15x + -6 = 0

Reorder the terms:
-4 + -6 + 9x + 15x + 169x2 + -49x2 = 0

Combine like terms: -4 + -6 = -10
-10 + 9x + 15x + 169x2 + -49x2 = 0

Combine like terms: 9x + 15x = 24x
-10 + 24x + 169x2 + -49x2 = 0

Combine like terms: 169x2 + -49x2 = 120x2
-10 + 24x + 120x2 = 0

Solving
-10 + 24x + 120x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 12x + 60x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 12x + 60x2)' equal to zero and attempt to solve:

Simplifying
-5 + 12x + 60x2 = 0

Solving
-5 + 12x + 60x2 = 0

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

Divide each side by '60'.
-0.08333333333 + 0.2x + x2 = 0.0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + 0.2x + 0.08333333333 + x2 = 0.0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + 0.2x + x2 = 0.0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + 0.2x + x2 = 0.0 + 0.08333333333
0.2x + x2 = 0.0 + 0.08333333333

Combine like terms: 0.0 + 0.08333333333 = 0.08333333333
0.2x + x2 = 0.08333333333

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 0.08333333333 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 0.08333333333 + 0.01

Combine like terms: 0.08333333333 + 0.01 = 0.09333333333
0.01 + 0.2x + x2 = 0.09333333333

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 0.09333333333

Calculate the square root of the right side: 0.305505046

Break this problem into two subproblems by setting 
(x + 0.1) equal to 0.305505046 and -0.305505046.


Subproblem 1
x + 0.1 = 0.305505046

Simplifying
x + 0.1 = 0.305505046

Reorder the terms:
0.1 + x = 0.305505046

Solving
0.1 + x = 0.305505046

Solving for variable 'x'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + x = 0.305505046 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = 0.305505046 + -0.1
x = 0.305505046 + -0.1

Combine like terms: 0.305505046 + -0.1 = 0.205505046
x = 0.205505046

Simplifying
x = 0.205505046


Subproblem 2
x + 0.1 = -0.305505046

Simplifying
x + 0.1 = -0.305505046

Reorder the terms:
0.1 + x = -0.305505046

Solving
0.1 + x = -0.305505046

Solving for variable 'x'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + x = -0.305505046 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = -0.305505046 + -0.1
x = -0.305505046 + -0.1

Combine like terms: -0.305505046 + -0.1 = -0.405505046
x = -0.405505046

Simplifying
x = -0.405505046


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.205505046, -0.405505046}
Solution
x = {0.205505046, -0.405505046}

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