5x(23-x)+1=

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Solution for 5x(23-x)+1= equation:


Simplifying
5x(23 + -1x) + 1 = 0
(23 * 5x + -1x * 5x) + 1 = 0
(115x + -5x2) + 1 = 0

Reorder the terms:
1 + 115x + -5x2 = 0

Solving
1 + 115x + -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'.
-0.2 + -23x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -23x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -23x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -23x + x2 = 0 + 0.2
-23x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-23x + x2 = 0.2

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = 0.2 + 132.25

Reorder the terms:
132.25 + -23x + x2 = 0.2 + 132.25

Combine like terms: 0.2 + 132.25 = 132.45
132.25 + -23x + x2 = 132.45

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 132.45

Calculate the square root of the right side: 11.508692367

Break this problem into two subproblems by setting 
(x + -11.5) equal to 11.508692367 and -11.508692367.

Subproblem 1

x + -11.5 = 11.508692367 Simplifying x + -11.5 = 11.508692367 Reorder the terms: -11.5 + x = 11.508692367 Solving -11.5 + x = 11.508692367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 11.508692367 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.508692367 + 11.5 x = 11.508692367 + 11.5 Combine like terms: 11.508692367 + 11.5 = 23.008692367 x = 23.008692367 Simplifying x = 23.008692367

Subproblem 2

x + -11.5 = -11.508692367 Simplifying x + -11.5 = -11.508692367 Reorder the terms: -11.5 + x = -11.508692367 Solving -11.5 + x = -11.508692367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -11.508692367 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.508692367 + 11.5 x = -11.508692367 + 11.5 Combine like terms: -11.508692367 + 11.5 = -0.008692367 x = -0.008692367 Simplifying x = -0.008692367

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.008692367, -0.008692367}

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