24x^2+4x-63=0

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Solution for 24x^2+4x-63=0 equation: 


Simplifying
24x2 + 4x + -63 = 0

Reorder the terms:
-63 + 4x + 24x2 = 0

Solving
-63 + 4x + 24x2 = 0

Solving for variable 'x'.

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

Divide each side by '24'.
-2.625 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '2.625' to each side of the equation.
-2.625 + 0.1666666667x + 2.625 + x2 = 0 + 2.625

Reorder the terms:
-2.625 + 2.625 + 0.1666666667x + x2 = 0 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + 0.1666666667x + x2 = 0 + 2.625
0.1666666667x + x2 = 0 + 2.625

Combine like terms: 0 + 2.625 = 2.625
0.1666666667x + x2 = 2.625

The x term is 0.1666666667x.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667x + 0.006944444447 + x2 = 2.625 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 2.625 + 0.006944444447

Combine like terms: 2.625 + 0.006944444447 = 2.631944444447
0.006944444447 + 0.1666666667x + x2 = 2.631944444447

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 2.631944444447

Calculate the square root of the right side: 1.622326861

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 1.622326861 and -1.622326861.


Subproblem 1
x + 0.08333333335 = 1.622326861

Simplifying
x + 0.08333333335 = 1.622326861

Reorder the terms:
0.08333333335 + x = 1.622326861

Solving
0.08333333335 + x = 1.622326861

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = 1.622326861 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = 1.622326861 + -0.08333333335
x = 1.622326861 + -0.08333333335

Combine like terms: 1.622326861 + -0.08333333335 = 1.53899352765
x = 1.53899352765

Simplifying
x = 1.53899352765


Subproblem 2
x + 0.08333333335 = -1.622326861

Simplifying
x + 0.08333333335 = -1.622326861

Reorder the terms:
0.08333333335 + x = -1.622326861

Solving
0.08333333335 + x = -1.622326861

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = -1.622326861 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = -1.622326861 + -0.08333333335
x = -1.622326861 + -0.08333333335

Combine like terms: -1.622326861 + -0.08333333335 = -1.70566019435
x = -1.70566019435

Simplifying
x = -1.70566019435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.53899352765, -1.70566019435}

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