8x^2+18x-9=0

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Solution for 8x^2+18x-9=0 equation: 


Simplifying
8x2 + 18x + -9 = 0

Reorder the terms:
-9 + 18x + 8x2 = 0

Solving
-9 + 18x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-1.125 + 2.25x + x2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + 2.25x + 1.125 + x2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + 2.25x + x2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + 2.25x + x2 = 0 + 1.125
2.25x + x2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
2.25x + x2 = 1.125

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = 1.125 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 1.125 + 1.265625

Combine like terms: 1.125 + 1.265625 = 2.390625
1.265625 + 2.25x + x2 = 2.390625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(x + 1.125) equal to 1.54616461 and -1.54616461.


Subproblem 1
x + 1.125 = 1.54616461

Simplifying
x + 1.125 = 1.54616461

Reorder the terms:
1.125 + x = 1.54616461

Solving
1.125 + x = 1.54616461

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = 1.54616461 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 1.54616461 + -1.125
x = 1.54616461 + -1.125

Combine like terms: 1.54616461 + -1.125 = 0.42116461
x = 0.42116461

Simplifying
x = 0.42116461


Subproblem 2
x + 1.125 = -1.54616461

Simplifying
x + 1.125 = -1.54616461

Reorder the terms:
1.125 + x = -1.54616461

Solving
1.125 + x = -1.54616461

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = -1.54616461 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -1.54616461 + -1.125
x = -1.54616461 + -1.125

Combine like terms: -1.54616461 + -1.125 = -2.67116461
x = -2.67116461

Simplifying
x = -2.67116461


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.42116461, -2.67116461}

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