-.225x^2+2.56x-5.54=0

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Solution for -.225x^2+2.56x-5.54=0 equation:


Simplifying
-0.225x2 + 2.56x + -5.54 = 0

Reorder the terms:
-5.54 + 2.56x + -0.225x2 = 0

Solving
-5.54 + 2.56x + -0.225x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.225 the coefficient of the squared term: 

Divide each side by '-0.225'.
24.62222222 + -11.37777778x + x2 = 0

Move the constant term to the right:

Add '-24.62222222' to each side of the equation.
24.62222222 + -11.37777778x + -24.62222222 + x2 = 0 + -24.62222222

Reorder the terms:
24.62222222 + -24.62222222 + -11.37777778x + x2 = 0 + -24.62222222

Combine like terms: 24.62222222 + -24.62222222 = 0.00000000
0.00000000 + -11.37777778x + x2 = 0 + -24.62222222
-11.37777778x + x2 = 0 + -24.62222222

Combine like terms: 0 + -24.62222222 = -24.62222222
-11.37777778x + x2 = -24.62222222

The x term is -11.37777778x.  Take half its coefficient (-5.68888889).
Square it (32.36345680) and add it to both sides.

Add '32.36345680' to each side of the equation.
-11.37777778x + 32.36345680 + x2 = -24.62222222 + 32.36345680

Reorder the terms:
32.36345680 + -11.37777778x + x2 = -24.62222222 + 32.36345680

Combine like terms: -24.62222222 + 32.36345680 = 7.74123458
32.36345680 + -11.37777778x + x2 = 7.74123458

Factor a perfect square on the left side:
(x + -5.68888889)(x + -5.68888889) = 7.74123458

Calculate the square root of the right side: 2.78230742

Break this problem into two subproblems by setting 
(x + -5.68888889) equal to 2.78230742 and -2.78230742.

Subproblem 1

x + -5.68888889 = 2.78230742 Simplifying x + -5.68888889 = 2.78230742 Reorder the terms: -5.68888889 + x = 2.78230742 Solving -5.68888889 + x = 2.78230742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.68888889' to each side of the equation. -5.68888889 + 5.68888889 + x = 2.78230742 + 5.68888889 Combine like terms: -5.68888889 + 5.68888889 = 0.00000000 0.00000000 + x = 2.78230742 + 5.68888889 x = 2.78230742 + 5.68888889 Combine like terms: 2.78230742 + 5.68888889 = 8.47119631 x = 8.47119631 Simplifying x = 8.47119631

Subproblem 2

x + -5.68888889 = -2.78230742 Simplifying x + -5.68888889 = -2.78230742 Reorder the terms: -5.68888889 + x = -2.78230742 Solving -5.68888889 + x = -2.78230742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.68888889' to each side of the equation. -5.68888889 + 5.68888889 + x = -2.78230742 + 5.68888889 Combine like terms: -5.68888889 + 5.68888889 = 0.00000000 0.00000000 + x = -2.78230742 + 5.68888889 x = -2.78230742 + 5.68888889 Combine like terms: -2.78230742 + 5.68888889 = 2.90658147 x = 2.90658147 Simplifying x = 2.90658147

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.47119631, 2.90658147}

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