x^2+0.24x-1=0

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Solution for x^2+0.24x-1=0 equation: 


Simplifying
x2 + 0.24x + -1 = 0

Reorder the terms:
-1 + 0.24x + x2 = 0

Solving
-1 + 0.24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.24x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.24x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.24x + x2 = 0 + 1
0.24x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.24x + x2 = 1

The x term is 0.24x.  Take half its coefficient (0.12).
Square it (0.0144) and add it to both sides.

Add '0.0144' to each side of the equation.
0.24x + 0.0144 + x2 = 1 + 0.0144

Reorder the terms:
0.0144 + 0.24x + x2 = 1 + 0.0144

Combine like terms: 1 + 0.0144 = 1.0144
0.0144 + 0.24x + x2 = 1.0144

Factor a perfect square on the left side:
(x + 0.12)(x + 0.12) = 1.0144

Calculate the square root of the right side: 1.007174265

Break this problem into two subproblems by setting 
(x + 0.12) equal to 1.007174265 and -1.007174265.


Subproblem 1
x + 0.12 = 1.007174265

Simplifying
x + 0.12 = 1.007174265

Reorder the terms:
0.12 + x = 1.007174265

Solving
0.12 + x = 1.007174265

Solving for variable 'x'.

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

Add '-0.12' to each side of the equation.
0.12 + -0.12 + x = 1.007174265 + -0.12

Combine like terms: 0.12 + -0.12 = 0.00
0.00 + x = 1.007174265 + -0.12
x = 1.007174265 + -0.12

Combine like terms: 1.007174265 + -0.12 = 0.887174265
x = 0.887174265

Simplifying
x = 0.887174265


Subproblem 2
x + 0.12 = -1.007174265

Simplifying
x + 0.12 = -1.007174265

Reorder the terms:
0.12 + x = -1.007174265

Solving
0.12 + x = -1.007174265

Solving for variable 'x'.

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

Add '-0.12' to each side of the equation.
0.12 + -0.12 + x = -1.007174265 + -0.12

Combine like terms: 0.12 + -0.12 = 0.00
0.00 + x = -1.007174265 + -0.12
x = -1.007174265 + -0.12

Combine like terms: -1.007174265 + -0.12 = -1.127174265
x = -1.127174265

Simplifying
x = -1.127174265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.887174265, -1.127174265}

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