x^2-0.25x=24

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Solution for x^2-0.25x=24 equation: 


Simplifying
x2 + -0.25x = 24

Reorder the terms:
-0.25x + x2 = 24

Solving
-0.25x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -0.25x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -0.25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -0.25x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -0.25x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -0.25x + x2 = 0 + 24
-0.25x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-0.25x + x2 = 24

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 = 24 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 24 + 0.015625

Combine like terms: 24 + 0.015625 = 24.015625
0.015625 + -0.25x + x2 = 24.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 24.015625

Calculate the square root of the right side: 4.900573946

Break this problem into two subproblems by setting 
(x + -0.125) equal to 4.900573946 and -4.900573946.


Subproblem 1
x + -0.125 = 4.900573946

Simplifying
x + -0.125 = 4.900573946

Reorder the terms:
-0.125 + x = 4.900573946

Solving
-0.125 + x = 4.900573946

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 = 4.900573946 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 4.900573946 + 0.125
x = 4.900573946 + 0.125

Combine like terms: 4.900573946 + 0.125 = 5.025573946
x = 5.025573946

Simplifying
x = 5.025573946


Subproblem 2
x + -0.125 = -4.900573946

Simplifying
x + -0.125 = -4.900573946

Reorder the terms:
-0.125 + x = -4.900573946

Solving
-0.125 + x = -4.900573946

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 = -4.900573946 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -4.900573946 + 0.125
x = -4.900573946 + 0.125

Combine like terms: -4.900573946 + 0.125 = -4.775573946
x = -4.775573946

Simplifying
x = -4.775573946


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.025573946, -4.775573946}

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