5x(2x-1)+5=13

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Solution for 5x(2x-1)+5=13 equation:


Simplifying
5x(2x + -1) + 5 = 13

Reorder the terms:
5x(-1 + 2x) + 5 = 13
(-1 * 5x + 2x * 5x) + 5 = 13
(-5x + 10x2) + 5 = 13

Reorder the terms:
5 + -5x + 10x2 = 13

Solving
5 + -5x + 10x2 = 13

Solving for variable 'x'.

Reorder the terms:
5 + -13 + -5x + 10x2 = 13 + -13

Combine like terms: 5 + -13 = -8
-8 + -5x + 10x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-8 + -5x + 10x2 = 0

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

Divide each side by '10'.
-0.8 + -0.5x + x2 = 0.0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -0.5x + 0.8 + x2 = 0.0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -0.5x + x2 = 0.0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -0.5x + x2 = 0.0 + 0.8
-0.5x + x2 = 0.0 + 0.8

Combine like terms: 0.0 + 0.8 = 0.8
-0.5x + x2 = 0.8

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.8 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.8 + 0.0625

Combine like terms: 0.8 + 0.0625 = 0.8625
0.0625 + -0.5x + x2 = 0.8625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.8625

Calculate the square root of the right side: 0.928708781

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.928708781 and -0.928708781.

Subproblem 1

x + -0.25 = 0.928708781 Simplifying x + -0.25 = 0.928708781 Reorder the terms: -0.25 + x = 0.928708781 Solving -0.25 + x = 0.928708781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.928708781 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.928708781 + 0.25 x = 0.928708781 + 0.25 Combine like terms: 0.928708781 + 0.25 = 1.178708781 x = 1.178708781 Simplifying x = 1.178708781

Subproblem 2

x + -0.25 = -0.928708781 Simplifying x + -0.25 = -0.928708781 Reorder the terms: -0.25 + x = -0.928708781 Solving -0.25 + x = -0.928708781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.928708781 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.928708781 + 0.25 x = -0.928708781 + 0.25 Combine like terms: -0.928708781 + 0.25 = -0.678708781 x = -0.678708781 Simplifying x = -0.678708781

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.178708781, -0.678708781}

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