x^2+1.44x-0.22=0

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Solution for x^2+1.44x-0.22=0 equation:


Simplifying
x2 + 1.44x + -0.22 = 0

Reorder the terms:
-0.22 + 1.44x + x2 = 0

Solving
-0.22 + 1.44x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.22' to each side of the equation.
-0.22 + 1.44x + 0.22 + x2 = 0 + 0.22

Reorder the terms:
-0.22 + 0.22 + 1.44x + x2 = 0 + 0.22

Combine like terms: -0.22 + 0.22 = 0.00
0.00 + 1.44x + x2 = 0 + 0.22
1.44x + x2 = 0 + 0.22

Combine like terms: 0 + 0.22 = 0.22
1.44x + x2 = 0.22

The x term is 1.44x.  Take half its coefficient (0.72).
Square it (0.5184) and add it to both sides.

Add '0.5184' to each side of the equation.
1.44x + 0.5184 + x2 = 0.22 + 0.5184

Reorder the terms:
0.5184 + 1.44x + x2 = 0.22 + 0.5184

Combine like terms: 0.22 + 0.5184 = 0.7384
0.5184 + 1.44x + x2 = 0.7384

Factor a perfect square on the left side:
(x + 0.72)(x + 0.72) = 0.7384

Calculate the square root of the right side: 0.859302042

Break this problem into two subproblems by setting 
(x + 0.72) equal to 0.859302042 and -0.859302042.

Subproblem 1

x + 0.72 = 0.859302042 Simplifying x + 0.72 = 0.859302042 Reorder the terms: 0.72 + x = 0.859302042 Solving 0.72 + x = 0.859302042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.72' to each side of the equation. 0.72 + -0.72 + x = 0.859302042 + -0.72 Combine like terms: 0.72 + -0.72 = 0.00 0.00 + x = 0.859302042 + -0.72 x = 0.859302042 + -0.72 Combine like terms: 0.859302042 + -0.72 = 0.139302042 x = 0.139302042 Simplifying x = 0.139302042

Subproblem 2

x + 0.72 = -0.859302042 Simplifying x + 0.72 = -0.859302042 Reorder the terms: 0.72 + x = -0.859302042 Solving 0.72 + x = -0.859302042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.72' to each side of the equation. 0.72 + -0.72 + x = -0.859302042 + -0.72 Combine like terms: 0.72 + -0.72 = 0.00 0.00 + x = -0.859302042 + -0.72 x = -0.859302042 + -0.72 Combine like terms: -0.859302042 + -0.72 = -1.579302042 x = -1.579302042 Simplifying x = -1.579302042

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.139302042, -1.579302042}

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