-5x^2-11x+18=0

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Solution for -5x^2-11x+18=0 equation:


Simplifying
-5x2 + -11x + 18 = 0

Reorder the terms:
18 + -11x + -5x2 = 0

Solving
18 + -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'.
-3.6 + 2.2x + x2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + 2.2x + 3.6 + x2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + 2.2x + x2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + 2.2x + x2 = 0 + 3.6
2.2x + x2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
2.2x + x2 = 3.6

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 = 3.6 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = 3.6 + 1.21

Combine like terms: 3.6 + 1.21 = 4.81
1.21 + 2.2x + x2 = 4.81

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 4.81

Calculate the square root of the right side: 2.19317122

Break this problem into two subproblems by setting 
(x + 1.1) equal to 2.19317122 and -2.19317122.

Subproblem 1

x + 1.1 = 2.19317122 Simplifying x + 1.1 = 2.19317122 Reorder the terms: 1.1 + x = 2.19317122 Solving 1.1 + x = 2.19317122 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 = 2.19317122 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 2.19317122 + -1.1 x = 2.19317122 + -1.1 Combine like terms: 2.19317122 + -1.1 = 1.09317122 x = 1.09317122 Simplifying x = 1.09317122

Subproblem 2

x + 1.1 = -2.19317122 Simplifying x + 1.1 = -2.19317122 Reorder the terms: 1.1 + x = -2.19317122 Solving 1.1 + x = -2.19317122 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 = -2.19317122 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -2.19317122 + -1.1 x = -2.19317122 + -1.1 Combine like terms: -2.19317122 + -1.1 = -3.29317122 x = -3.29317122 Simplifying x = -3.29317122

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.09317122, -3.29317122}

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