2x^2+17x-45=0

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Solution for 2x^2+17x-45=0 equation:


Simplifying
2x2 + 17x + -45 = 0

Reorder the terms:
-45 + 17x + 2x2 = 0

Solving
-45 + 17x + 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'.
-22.5 + 8.5x + x2 = 0

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + 8.5x + 22.5 + x2 = 0 + 22.5

Reorder the terms:
-22.5 + 22.5 + 8.5x + x2 = 0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + 8.5x + x2 = 0 + 22.5
8.5x + x2 = 0 + 22.5

Combine like terms: 0 + 22.5 = 22.5
8.5x + x2 = 22.5

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = 22.5 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = 22.5 + 18.0625

Combine like terms: 22.5 + 18.0625 = 40.5625
18.0625 + 8.5x + x2 = 40.5625

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 40.5625

Calculate the square root of the right side: 6.368869601

Break this problem into two subproblems by setting 
(x + 4.25) equal to 6.368869601 and -6.368869601.

Subproblem 1

x + 4.25 = 6.368869601 Simplifying x + 4.25 = 6.368869601 Reorder the terms: 4.25 + x = 6.368869601 Solving 4.25 + x = 6.368869601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 6.368869601 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 6.368869601 + -4.25 x = 6.368869601 + -4.25 Combine like terms: 6.368869601 + -4.25 = 2.118869601 x = 2.118869601 Simplifying x = 2.118869601

Subproblem 2

x + 4.25 = -6.368869601 Simplifying x + 4.25 = -6.368869601 Reorder the terms: 4.25 + x = -6.368869601 Solving 4.25 + x = -6.368869601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -6.368869601 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -6.368869601 + -4.25 x = -6.368869601 + -4.25 Combine like terms: -6.368869601 + -4.25 = -10.618869601 x = -10.618869601 Simplifying x = -10.618869601

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.118869601, -10.618869601}

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