4x^2+27x-23=-8x+2

Solution for 4x^2+27x-23=-8x+2 equation:

Simplifying
4x2 + 27x + -23 = -8x + 2

Reorder the terms:
-23 + 27x + 4x2 = -8x + 2

Reorder the terms:
-23 + 27x + 4x2 = 2 + -8x

Solving
-23 + 27x + 4x2 = 2 + -8x

Solving for variable 'x'.

Reorder the terms:
-23 + -2 + 27x + 8x + 4x2 = 2 + -8x + -2 + 8x

Combine like terms: -23 + -2 = -25
-25 + 27x + 8x + 4x2 = 2 + -8x + -2 + 8x

Combine like terms: 27x + 8x = 35x
-25 + 35x + 4x2 = 2 + -8x + -2 + 8x

Reorder the terms:
-25 + 35x + 4x2 = 2 + -2 + -8x + 8x

Combine like terms: 2 + -2 = 0
-25 + 35x + 4x2 = 0 + -8x + 8x
-25 + 35x + 4x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-25 + 35x + 4x2 = 0

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

Divide each side by '4'.
-6.25 + 8.75x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 8.75x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 8.75x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 8.75x + x2 = 0 + 6.25
8.75x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
8.75x + x2 = 6.25

The x term is 8.75x.  Take half its coefficient (4.375).
Square it (19.140625) and add it to both sides.

Add '19.140625' to each side of the equation.
8.75x + 19.140625 + x2 = 6.25 + 19.140625

Reorder the terms:
19.140625 + 8.75x + x2 = 6.25 + 19.140625

Combine like terms: 6.25 + 19.140625 = 25.390625
19.140625 + 8.75x + x2 = 25.390625

Factor a perfect square on the left side:
(x + 4.375)(x + 4.375) = 25.390625

Calculate the square root of the right side: 5.038911093

Break this problem into two subproblems by setting 
(x + 4.375) equal to 5.038911093 and -5.038911093.

Subproblem 1
x + 4.375 = 5.038911093

Simplifying
x + 4.375 = 5.038911093

Reorder the terms:
4.375 + x = 5.038911093

Solving
4.375 + x = 5.038911093

Solving for variable 'x'.

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

Add '-4.375' to each side of the equation.
4.375 + -4.375 + x = 5.038911093 + -4.375

Combine like terms: 4.375 + -4.375 = 0.000
0.000 + x = 5.038911093 + -4.375
x = 5.038911093 + -4.375

Combine like terms: 5.038911093 + -4.375 = 0.663911093
x = 0.663911093

Simplifying
x = 0.663911093

Subproblem 2
x + 4.375 = -5.038911093

Simplifying
x + 4.375 = -5.038911093

Reorder the terms:
4.375 + x = -5.038911093

Solving
4.375 + x = -5.038911093

Solving for variable 'x'.

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

Add '-4.375' to each side of the equation.
4.375 + -4.375 + x = -5.038911093 + -4.375

Combine like terms: 4.375 + -4.375 = 0.000
0.000 + x = -5.038911093 + -4.375
x = -5.038911093 + -4.375

Combine like terms: -5.038911093 + -4.375 = -9.413911093
x = -9.413911093

Simplifying
x = -9.413911093

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.663911093, -9.413911093}