-5X^2-11X+8=0

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Solution for -5X^2-11X+8=0 equation:


Simplifying
-5X2 + -11X + 8 = 0

Reorder the terms:
8 + -11X + -5X2 = 0

Solving
8 + -11X + -5X2 = 0

Solving for variable 'X'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.6 + 2.2X + X2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 2.2X + 1.6 + X2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 2.2X + X2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 2.2X + X2 = 0 + 1.6
2.2X + X2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
2.2X + X2 = 1.6

The X term is 2.2X.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2X + 1.21 + X2 = 1.6 + 1.21

Reorder the terms:
1.21 + 2.2X + X2 = 1.6 + 1.21

Combine like terms: 1.6 + 1.21 = 2.81
1.21 + 2.2X + X2 = 2.81

Factor a perfect square on the left side:
(X + 1.1)(X + 1.1) = 2.81

Calculate the square root of the right side: 1.676305461

Break this problem into two subproblems by setting 
(X + 1.1) equal to 1.676305461 and -1.676305461.

Subproblem 1

X + 1.1 = 1.676305461 Simplifying X + 1.1 = 1.676305461 Reorder the terms: 1.1 + X = 1.676305461 Solving 1.1 + X = 1.676305461 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + X = 1.676305461 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + X = 1.676305461 + -1.1 X = 1.676305461 + -1.1 Combine like terms: 1.676305461 + -1.1 = 0.576305461 X = 0.576305461 Simplifying X = 0.576305461

Subproblem 2

X + 1.1 = -1.676305461 Simplifying X + 1.1 = -1.676305461 Reorder the terms: 1.1 + X = -1.676305461 Solving 1.1 + X = -1.676305461 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + X = -1.676305461 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + X = -1.676305461 + -1.1 X = -1.676305461 + -1.1 Combine like terms: -1.676305461 + -1.1 = -2.776305461 X = -2.776305461 Simplifying X = -2.776305461

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.576305461, -2.776305461}

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