5.5x^2-x-2.3=

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Solution for 5.5x^2-x-2.3= equation:


Simplifying
5.5x2 + -1x + -2.3 = 0

Reorder the terms:
-2.3 + -1x + 5.5x2 = 0

Solving
-2.3 + -1x + 5.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5.5'.
-0.4181818182 + -0.1818181818x + x2 = 0

Move the constant term to the right:

Add '0.4181818182' to each side of the equation.
-0.4181818182 + -0.1818181818x + 0.4181818182 + x2 = 0 + 0.4181818182

Reorder the terms:
-0.4181818182 + 0.4181818182 + -0.1818181818x + x2 = 0 + 0.4181818182

Combine like terms: -0.4181818182 + 0.4181818182 = 0.0000000000
0.0000000000 + -0.1818181818x + x2 = 0 + 0.4181818182
-0.1818181818x + x2 = 0 + 0.4181818182

Combine like terms: 0 + 0.4181818182 = 0.4181818182
-0.1818181818x + x2 = 0.4181818182

The x term is -0.1818181818x.  Take half its coefficient (-0.0909090909).
Square it (0.008264462808) and add it to both sides.

Add '0.008264462808' to each side of the equation.
-0.1818181818x + 0.008264462808 + x2 = 0.4181818182 + 0.008264462808

Reorder the terms:
0.008264462808 + -0.1818181818x + x2 = 0.4181818182 + 0.008264462808

Combine like terms: 0.4181818182 + 0.008264462808 = 0.426446281008
0.008264462808 + -0.1818181818x + x2 = 0.426446281008

Factor a perfect square on the left side:
(x + -0.0909090909)(x + -0.0909090909) = 0.426446281008

Calculate the square root of the right side: 0.653028545

Break this problem into two subproblems by setting 
(x + -0.0909090909) equal to 0.653028545 and -0.653028545.

Subproblem 1

x + -0.0909090909 = 0.653028545 Simplifying x + -0.0909090909 = 0.653028545 Reorder the terms: -0.0909090909 + x = 0.653028545 Solving -0.0909090909 + x = 0.653028545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = 0.653028545 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = 0.653028545 + 0.0909090909 x = 0.653028545 + 0.0909090909 Combine like terms: 0.653028545 + 0.0909090909 = 0.7439376359 x = 0.7439376359 Simplifying x = 0.7439376359

Subproblem 2

x + -0.0909090909 = -0.653028545 Simplifying x + -0.0909090909 = -0.653028545 Reorder the terms: -0.0909090909 + x = -0.653028545 Solving -0.0909090909 + x = -0.653028545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = -0.653028545 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = -0.653028545 + 0.0909090909 x = -0.653028545 + 0.0909090909 Combine like terms: -0.653028545 + 0.0909090909 = -0.5621194541 x = -0.5621194541 Simplifying x = -0.5621194541

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7439376359, -0.5621194541}

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