2x^2+4.5x-17=0

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Solution for 2x^2+4.5x-17=0 equation: 


Simplifying
2x2 + 4.5x + -17 = 0

Reorder the terms:
-17 + 4.5x + 2x2 = 0

Solving
-17 + 4.5x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-8.5 + 2.25x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 2.25x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 2.25x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 2.25x + x2 = 0 + 8.5
2.25x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
2.25x + x2 = 8.5

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 = 8.5 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 8.5 + 1.265625

Combine like terms: 8.5 + 1.265625 = 9.765625
1.265625 + 2.25x + x2 = 9.765625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 9.765625

Calculate the square root of the right side: 3.125

Break this problem into two subproblems by setting 
(x + 1.125) equal to 3.125 and -3.125.


Subproblem 1
x + 1.125 = 3.125

Simplifying
x + 1.125 = 3.125

Reorder the terms:
1.125 + x = 3.125

Solving
1.125 + x = 3.125

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 = 3.125 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 3.125 + -1.125
x = 3.125 + -1.125

Combine like terms: 3.125 + -1.125 = 2
x = 2

Simplifying
x = 2


Subproblem 2
x + 1.125 = -3.125

Simplifying
x + 1.125 = -3.125

Reorder the terms:
1.125 + x = -3.125

Solving
1.125 + x = -3.125

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 = -3.125 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -3.125 + -1.125
x = -3.125 + -1.125

Combine like terms: -3.125 + -1.125 = -4.25
x = -4.25

Simplifying
x = -4.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -4.25}

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