2x(5x+1)=11

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Solution for 2x(5x+1)=11 equation:


Simplifying
2x(5x + 1) = 11

Reorder the terms:
2x(1 + 5x) = 11
(1 * 2x + 5x * 2x) = 11
(2x + 10x2) = 11

Solving
2x + 10x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + 2x + 10x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 2x + 10x2 = 0

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

Divide each side by '10'.
-1.1 + 0.2x + x2 = 0.0

Move the constant term to the right:

Add '1.1' to each side of the equation.
-1.1 + 0.2x + 1.1 + x2 = 0.0 + 1.1

Reorder the terms:
-1.1 + 1.1 + 0.2x + x2 = 0.0 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + 0.2x + x2 = 0.0 + 1.1
0.2x + x2 = 0.0 + 1.1

Combine like terms: 0.0 + 1.1 = 1.1
0.2x + x2 = 1.1

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 1.1 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 1.1 + 0.01

Combine like terms: 1.1 + 0.01 = 1.11
0.01 + 0.2x + x2 = 1.11

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 1.11

Calculate the square root of the right side: 1.053565375

Break this problem into two subproblems by setting 
(x + 0.1) equal to 1.053565375 and -1.053565375.

Subproblem 1

x + 0.1 = 1.053565375 Simplifying x + 0.1 = 1.053565375 Reorder the terms: 0.1 + x = 1.053565375 Solving 0.1 + x = 1.053565375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 1.053565375 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.053565375 + -0.1 x = 1.053565375 + -0.1 Combine like terms: 1.053565375 + -0.1 = 0.953565375 x = 0.953565375 Simplifying x = 0.953565375

Subproblem 2

x + 0.1 = -1.053565375 Simplifying x + 0.1 = -1.053565375 Reorder the terms: 0.1 + x = -1.053565375 Solving 0.1 + x = -1.053565375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -1.053565375 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.053565375 + -0.1 x = -1.053565375 + -0.1 Combine like terms: -1.053565375 + -0.1 = -1.153565375 x = -1.153565375 Simplifying x = -1.153565375

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.953565375, -1.153565375}

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