10x^2-5x=9x+8

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Solution for 10x^2-5x=9x+8 equation: 


Simplifying
10x2 + -5x = 9x + 8

Reorder the terms:
-5x + 10x2 = 9x + 8

Reorder the terms:
-5x + 10x2 = 8 + 9x

Solving
-5x + 10x2 = 8 + 9x

Solving for variable 'x'.

Reorder the terms:
-8 + -5x + -9x + 10x2 = 8 + 9x + -8 + -9x

Combine like terms: -5x + -9x = -14x
-8 + -14x + 10x2 = 8 + 9x + -8 + -9x

Reorder the terms:
-8 + -14x + 10x2 = 8 + -8 + 9x + -9x

Combine like terms: 8 + -8 = 0
-8 + -14x + 10x2 = 0 + 9x + -9x
-8 + -14x + 10x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-8 + -14x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -7x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -7x + 5x2)' equal to zero and attempt to solve:

Simplifying
-4 + -7x + 5x2 = 0

Solving
-4 + -7x + 5x2 = 0

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

Divide each side by '5'.
-0.8 + -1.4x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -1.4x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -1.4x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -1.4x + x2 = 0 + 0.8
-1.4x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-1.4x + x2 = 0.8

The x term is -1.4x.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 0.8 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 0.8 + 0.49

Combine like terms: 0.8 + 0.49 = 1.29
0.49 + -1.4x + x2 = 1.29

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 1.29

Calculate the square root of the right side: 1.135781669

Break this problem into two subproblems by setting 
(x + -0.7) equal to 1.135781669 and -1.135781669.


Subproblem 1
x + -0.7 = 1.135781669

Simplifying
x + -0.7 = 1.135781669

Reorder the terms:
-0.7 + x = 1.135781669

Solving
-0.7 + x = 1.135781669

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.135781669 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.135781669 + 0.7
x = 1.135781669 + 0.7

Combine like terms: 1.135781669 + 0.7 = 1.835781669
x = 1.835781669

Simplifying
x = 1.835781669


Subproblem 2
x + -0.7 = -1.135781669

Simplifying
x + -0.7 = -1.135781669

Reorder the terms:
-0.7 + x = -1.135781669

Solving
-0.7 + x = -1.135781669

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.135781669 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.135781669 + 0.7
x = -1.135781669 + 0.7

Combine like terms: -1.135781669 + 0.7 = -0.435781669
x = -0.435781669

Simplifying
x = -0.435781669


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.835781669, -0.435781669}
Solution
x = {1.835781669, -0.435781669}

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