10x^2+17x-38=0

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Solution for 10x^2+17x-38=0 equation: 


Simplifying
10x2 + 17x + -38 = 0

Reorder the terms:
-38 + 17x + 10x2 = 0

Solving
-38 + 17x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-3.8 + 1.7x + x2 = 0

Move the constant term to the right:

Add '3.8' to each side of the equation.
-3.8 + 1.7x + 3.8 + x2 = 0 + 3.8

Reorder the terms:
-3.8 + 3.8 + 1.7x + x2 = 0 + 3.8

Combine like terms: -3.8 + 3.8 = 0.0
0.0 + 1.7x + x2 = 0 + 3.8
1.7x + x2 = 0 + 3.8

Combine like terms: 0 + 3.8 = 3.8
1.7x + x2 = 3.8

The x term is 1.7x.  Take half its coefficient (0.85).
Square it (0.7225) and add it to both sides.

Add '0.7225' to each side of the equation.
1.7x + 0.7225 + x2 = 3.8 + 0.7225

Reorder the terms:
0.7225 + 1.7x + x2 = 3.8 + 0.7225

Combine like terms: 3.8 + 0.7225 = 4.5225
0.7225 + 1.7x + x2 = 4.5225

Factor a perfect square on the left side:
(x + 0.85)(x + 0.85) = 4.5225

Calculate the square root of the right side: 2.126617032

Break this problem into two subproblems by setting 
(x + 0.85) equal to 2.126617032 and -2.126617032.


Subproblem 1
x + 0.85 = 2.126617032

Simplifying
x + 0.85 = 2.126617032

Reorder the terms:
0.85 + x = 2.126617032

Solving
0.85 + x = 2.126617032

Solving for variable 'x'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + x = 2.126617032 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + x = 2.126617032 + -0.85
x = 2.126617032 + -0.85

Combine like terms: 2.126617032 + -0.85 = 1.276617032
x = 1.276617032

Simplifying
x = 1.276617032


Subproblem 2
x + 0.85 = -2.126617032

Simplifying
x + 0.85 = -2.126617032

Reorder the terms:
0.85 + x = -2.126617032

Solving
0.85 + x = -2.126617032

Solving for variable 'x'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + x = -2.126617032 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + x = -2.126617032 + -0.85
x = -2.126617032 + -0.85

Combine like terms: -2.126617032 + -0.85 = -2.976617032
x = -2.976617032

Simplifying
x = -2.976617032


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.276617032, -2.976617032}

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