0.24x^2-4.66x-10.51=0

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Solution for 0.24x^2-4.66x-10.51=0 equation: 


Simplifying
0.24x2 + -4.66x + -10.51 = 0

Reorder the terms:
-10.51 + -4.66x + 0.24x2 = 0

Solving
-10.51 + -4.66x + 0.24x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.24'.
-43.79166667 + -19.41666667x + x2 = 0

Move the constant term to the right:

Add '43.79166667' to each side of the equation.
-43.79166667 + -19.41666667x + 43.79166667 + x2 = 0 + 43.79166667

Reorder the terms:
-43.79166667 + 43.79166667 + -19.41666667x + x2 = 0 + 43.79166667

Combine like terms: -43.79166667 + 43.79166667 = 0.00000000
0.00000000 + -19.41666667x + x2 = 0 + 43.79166667
-19.41666667x + x2 = 0 + 43.79166667

Combine like terms: 0 + 43.79166667 = 43.79166667
-19.41666667x + x2 = 43.79166667

The x term is -19.41666667x.  Take half its coefficient (-9.708333335).
Square it (94.25173614) and add it to both sides.

Add '94.25173614' to each side of the equation.
-19.41666667x + 94.25173614 + x2 = 43.79166667 + 94.25173614

Reorder the terms:
94.25173614 + -19.41666667x + x2 = 43.79166667 + 94.25173614

Combine like terms: 43.79166667 + 94.25173614 = 138.04340281
94.25173614 + -19.41666667x + x2 = 138.04340281

Factor a perfect square on the left side:
(x + -9.708333335)(x + -9.708333335) = 138.04340281

Calculate the square root of the right side: 11.749187326

Break this problem into two subproblems by setting 
(x + -9.708333335) equal to 11.749187326 and -11.749187326.


Subproblem 1
x + -9.708333335 = 11.749187326

Simplifying
x + -9.708333335 = 11.749187326

Reorder the terms:
-9.708333335 + x = 11.749187326

Solving
-9.708333335 + x = 11.749187326

Solving for variable 'x'.

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

Add '9.708333335' to each side of the equation.
-9.708333335 + 9.708333335 + x = 11.749187326 + 9.708333335

Combine like terms: -9.708333335 + 9.708333335 = 0.000000000
0.000000000 + x = 11.749187326 + 9.708333335
x = 11.749187326 + 9.708333335

Combine like terms: 11.749187326 + 9.708333335 = 21.457520661
x = 21.457520661

Simplifying
x = 21.457520661


Subproblem 2
x + -9.708333335 = -11.749187326

Simplifying
x + -9.708333335 = -11.749187326

Reorder the terms:
-9.708333335 + x = -11.749187326

Solving
-9.708333335 + x = -11.749187326

Solving for variable 'x'.

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

Add '9.708333335' to each side of the equation.
-9.708333335 + 9.708333335 + x = -11.749187326 + 9.708333335

Combine like terms: -9.708333335 + 9.708333335 = 0.000000000
0.000000000 + x = -11.749187326 + 9.708333335
x = -11.749187326 + 9.708333335

Combine like terms: -11.749187326 + 9.708333335 = -2.040853991
x = -2.040853991

Simplifying
x = -2.040853991


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.457520661, -2.040853991}

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