8x^2-7x+42x-49=33x-17

Solution for 8x^2-7x+42x-49=33x-17 equation:

Simplifying
8x2 + -7x + 42x + -49 = 33x + -17

Reorder the terms:
-49 + -7x + 42x + 8x2 = 33x + -17

Combine like terms: -7x + 42x = 35x
-49 + 35x + 8x2 = 33x + -17

Reorder the terms:
-49 + 35x + 8x2 = -17 + 33x

Solving
-49 + 35x + 8x2 = -17 + 33x

Solving for variable 'x'.

Reorder the terms:
-49 + 17 + 35x + -33x + 8x2 = -17 + 33x + 17 + -33x

Combine like terms: -49 + 17 = -32
-32 + 35x + -33x + 8x2 = -17 + 33x + 17 + -33x

Combine like terms: 35x + -33x = 2x
-32 + 2x + 8x2 = -17 + 33x + 17 + -33x

Reorder the terms:
-32 + 2x + 8x2 = -17 + 17 + 33x + -33x

Combine like terms: -17 + 17 = 0
-32 + 2x + 8x2 = 0 + 33x + -33x
-32 + 2x + 8x2 = 33x + -33x

Combine like terms: 33x + -33x = 0
-32 + 2x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-16 + x + 4x2)' equal to zero and attempt to solve:

Simplifying
-16 + x + 4x2 = 0

Solving
-16 + x + 4x2 = 0

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

Divide each side by '4'.
-4 + 0.25x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.25x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.25x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.25x + x2 = 0 + 4
0.25x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.25x + x2 = 4

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25x + 0.25 + x2 = 4 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + 0.25x + x2 = 4.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
x + 0.5 = 2.061552813

Simplifying
x + 0.5 = 2.061552813

Reorder the terms:
0.5 + x = 2.061552813

Solving
0.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.061552813 + -0.5
x = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
x = 1.561552813

Simplifying
x = 1.561552813

Subproblem 2
x + 0.5 = -2.061552813

Simplifying
x + 0.5 = -2.061552813

Reorder the terms:
0.5 + x = -2.061552813

Solving
0.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.061552813 + -0.5
x = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
x = -2.561552813

Simplifying
x = -2.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.561552813, -2.561552813}
Solution
x = {1.561552813, -2.561552813}