17x^2+4=(x+3)(2x+7)-x+8

Solution for 17x^2+4=(x+3)(2x+7)-x+8 equation:

Simplifying
17x2 + 4 = (x + 3)(2x + 7) + -1x + 8

Reorder the terms:
4 + 17x2 = (x + 3)(2x + 7) + -1x + 8

Reorder the terms:
4 + 17x2 = (3 + x)(2x + 7) + -1x + 8

Reorder the terms:
4 + 17x2 = (3 + x)(7 + 2x) + -1x + 8

Multiply (3 + x) * (7 + 2x)
4 + 17x2 = (3(7 + 2x) + x(7 + 2x)) + -1x + 8
4 + 17x2 = ((7 * 3 + 2x * 3) + x(7 + 2x)) + -1x + 8
4 + 17x2 = ((21 + 6x) + x(7 + 2x)) + -1x + 8
4 + 17x2 = (21 + 6x + (7 * x + 2x * x)) + -1x + 8
4 + 17x2 = (21 + 6x + (7x + 2x2)) + -1x + 8

Combine like terms: 6x + 7x = 13x
4 + 17x2 = (21 + 13x + 2x2) + -1x + 8

Reorder the terms:
4 + 17x2 = 21 + 8 + 13x + -1x + 2x2

Combine like terms: 21 + 8 = 29
4 + 17x2 = 29 + 13x + -1x + 2x2

Combine like terms: 13x + -1x = 12x
4 + 17x2 = 29 + 12x + 2x2

Solving
4 + 17x2 = 29 + 12x + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + -29 + -12x + 17x2 + -2x2 = 29 + 12x + 2x2 + -29 + -12x + -2x2

Combine like terms: 4 + -29 = -25
-25 + -12x + 17x2 + -2x2 = 29 + 12x + 2x2 + -29 + -12x + -2x2

Combine like terms: 17x2 + -2x2 = 15x2
-25 + -12x + 15x2 = 29 + 12x + 2x2 + -29 + -12x + -2x2

Reorder the terms:
-25 + -12x + 15x2 = 29 + -29 + 12x + -12x + 2x2 + -2x2

Combine like terms: 29 + -29 = 0
-25 + -12x + 15x2 = 0 + 12x + -12x + 2x2 + -2x2
-25 + -12x + 15x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
-25 + -12x + 15x2 = 0 + 2x2 + -2x2
-25 + -12x + 15x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-25 + -12x + 15x2 = 0

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

Divide each side by '15'.
-1.666666667 + -0.8x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -0.8x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -0.8x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -0.8x + x2 = 0 + 1.666666667
-0.8x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-0.8x + x2 = 1.666666667

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 1.666666667 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 1.666666667 + 0.16

Combine like terms: 1.666666667 + 0.16 = 1.826666667
0.16 + -0.8x + x2 = 1.826666667

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 1.826666667

Calculate the square root of the right side: 1.351542329

Break this problem into two subproblems by setting 
(x + -0.4) equal to 1.351542329 and -1.351542329.

Subproblem 1
x + -0.4 = 1.351542329

Simplifying
x + -0.4 = 1.351542329

Reorder the terms:
-0.4 + x = 1.351542329

Solving
-0.4 + x = 1.351542329

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 1.351542329 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 1.351542329 + 0.4
x = 1.351542329 + 0.4

Combine like terms: 1.351542329 + 0.4 = 1.751542329
x = 1.751542329

Simplifying
x = 1.751542329

Subproblem 2
x + -0.4 = -1.351542329

Simplifying
x + -0.4 = -1.351542329

Reorder the terms:
-0.4 + x = -1.351542329

Solving
-0.4 + x = -1.351542329

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -1.351542329 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -1.351542329 + 0.4
x = -1.351542329 + 0.4

Combine like terms: -1.351542329 + 0.4 = -0.951542329
x = -0.951542329

Simplifying
x = -0.951542329

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.751542329, -0.951542329}