5x^2+11x-5=0

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


Simplifying
5x2 + 11x + -5 = 0

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

Solving
-5 + 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 + 2.2x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.2x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.2x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.2x + x2 = 0 + 1
2.2x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.2x + x2 = 1

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 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = 1 + 1.21

Combine like terms: 1 + 1.21 = 2.21
1.21 + 2.2x + x2 = 2.21

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 2.21

Calculate the square root of the right side: 1.486606875

Break this problem into two subproblems by setting 
(x + 1.1) equal to 1.486606875 and -1.486606875.

Subproblem 1

x + 1.1 = 1.486606875 Simplifying x + 1.1 = 1.486606875 Reorder the terms: 1.1 + x = 1.486606875 Solving 1.1 + x = 1.486606875 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 = 1.486606875 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.486606875 + -1.1 x = 1.486606875 + -1.1 Combine like terms: 1.486606875 + -1.1 = 0.386606875 x = 0.386606875 Simplifying x = 0.386606875

Subproblem 2

x + 1.1 = -1.486606875 Simplifying x + 1.1 = -1.486606875 Reorder the terms: 1.1 + x = -1.486606875 Solving 1.1 + x = -1.486606875 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 = -1.486606875 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.486606875 + -1.1 x = -1.486606875 + -1.1 Combine like terms: -1.486606875 + -1.1 = -2.586606875 x = -2.586606875 Simplifying x = -2.586606875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.386606875, -2.586606875}

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