4.9x^2-18x-23=0

Solution for 4.9x^2-18x-23=0 equation:

Simplifying
4.9x2 + -18x + -23 = 0

Reorder the terms:
-23 + -18x + 4.9x2 = 0

Solving
-23 + -18x + 4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.9'.
-4.693877551 + -3.673469388x + x2 = 0

Move the constant term to the right:

Add '4.693877551' to each side of the equation.
-4.693877551 + -3.673469388x + 4.693877551 + x2 = 0 + 4.693877551

Reorder the terms:
-4.693877551 + 4.693877551 + -3.673469388x + x2 = 0 + 4.693877551

Combine like terms: -4.693877551 + 4.693877551 = 0.000000000
0.000000000 + -3.673469388x + x2 = 0 + 4.693877551
-3.673469388x + x2 = 0 + 4.693877551

Combine like terms: 0 + 4.693877551 = 4.693877551
-3.673469388x + x2 = 4.693877551

The x term is -3.673469388x.  Take half its coefficient (-1.836734694).
Square it (3.373594336) and add it to both sides.

Add '3.373594336' to each side of the equation.
-3.673469388x + 3.373594336 + x2 = 4.693877551 + 3.373594336

Reorder the terms:
3.373594336 + -3.673469388x + x2 = 4.693877551 + 3.373594336

Combine like terms: 4.693877551 + 3.373594336 = 8.067471887
3.373594336 + -3.673469388x + x2 = 8.067471887

Factor a perfect square on the left side:
(x + -1.836734694)(x + -1.836734694) = 8.067471887

Calculate the square root of the right side: 2.840329538

Break this problem into two subproblems by setting 
(x + -1.836734694) equal to 2.840329538 and -2.840329538.

Subproblem 1
x + -1.836734694 = 2.840329538

Simplifying
x + -1.836734694 = 2.840329538

Reorder the terms:
-1.836734694 + x = 2.840329538

Solving
-1.836734694 + x = 2.840329538

Solving for variable 'x'.

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

Add '1.836734694' to each side of the equation.
-1.836734694 + 1.836734694 + x = 2.840329538 + 1.836734694

Combine like terms: -1.836734694 + 1.836734694 = 0.000000000
0.000000000 + x = 2.840329538 + 1.836734694
x = 2.840329538 + 1.836734694

Combine like terms: 2.840329538 + 1.836734694 = 4.677064232
x = 4.677064232

Simplifying
x = 4.677064232

Subproblem 2
x + -1.836734694 = -2.840329538

Simplifying
x + -1.836734694 = -2.840329538

Reorder the terms:
-1.836734694 + x = -2.840329538

Solving
-1.836734694 + x = -2.840329538

Solving for variable 'x'.

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

Add '1.836734694' to each side of the equation.
-1.836734694 + 1.836734694 + x = -2.840329538 + 1.836734694

Combine like terms: -1.836734694 + 1.836734694 = 0.000000000
0.000000000 + x = -2.840329538 + 1.836734694
x = -2.840329538 + 1.836734694

Combine like terms: -2.840329538 + 1.836734694 = -1.003594844
x = -1.003594844

Simplifying
x = -1.003594844

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.677064232, -1.003594844}