4x^2-23x+17x=-7x+10

Solution for 4x^2-23x+17x=-7x+10 equation:

Simplifying
4x2 + -23x + 17x = -7x + 10

Reorder the terms:
-23x + 17x + 4x2 = -7x + 10

Combine like terms: -23x + 17x = -6x
-6x + 4x2 = -7x + 10

Reorder the terms:
-6x + 4x2 = 10 + -7x

Solving
-6x + 4x2 = 10 + -7x

Solving for variable 'x'.

Reorder the terms:
-10 + -6x + 7x + 4x2 = 10 + -7x + -10 + 7x

Combine like terms: -6x + 7x = 1x
-10 + 1x + 4x2 = 10 + -7x + -10 + 7x

Reorder the terms:
-10 + 1x + 4x2 = 10 + -10 + -7x + 7x

Combine like terms: 10 + -10 = 0
-10 + 1x + 4x2 = 0 + -7x + 7x
-10 + 1x + 4x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-10 + 1x + 4x2 = 0

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

Divide each side by '4'.
-2.5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.25x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.25x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.25x + x2 = 0 + 2.5
0.25x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
0.25x + x2 = 2.5

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 2.5 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 2.5 + 0.015625

Combine like terms: 2.5 + 0.015625 = 2.515625
0.015625 + 0.25x + x2 = 2.515625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 2.515625

Calculate the square root of the right side: 1.586072193

Break this problem into two subproblems by setting 
(x + 0.125) equal to 1.586072193 and -1.586072193.

Subproblem 1
x + 0.125 = 1.586072193

Simplifying
x + 0.125 = 1.586072193

Reorder the terms:
0.125 + x = 1.586072193

Solving
0.125 + x = 1.586072193

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 1.586072193 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 1.586072193 + -0.125
x = 1.586072193 + -0.125

Combine like terms: 1.586072193 + -0.125 = 1.461072193
x = 1.461072193

Simplifying
x = 1.461072193

Subproblem 2
x + 0.125 = -1.586072193

Simplifying
x + 0.125 = -1.586072193

Reorder the terms:
0.125 + x = -1.586072193

Solving
0.125 + x = -1.586072193

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -1.586072193 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -1.586072193 + -0.125
x = -1.586072193 + -0.125

Combine like terms: -1.586072193 + -0.125 = -1.711072193
x = -1.711072193

Simplifying
x = -1.711072193

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.461072193, -1.711072193}