x(5x-36)=26

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Solution for x(5x-36)=26 equation:


Simplifying
x(5x + -36) = 26

Reorder the terms:
x(-36 + 5x) = 26
(-36 * x + 5x * x) = 26
(-36x + 5x2) = 26

Solving
-36x + 5x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + -36x + 5x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + -36x + 5x2 = 0

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

Divide each side by '5'.
-5.2 + -7.2x + x2 = 0

Move the constant term to the right:

Add '5.2' to each side of the equation.
-5.2 + -7.2x + 5.2 + x2 = 0 + 5.2

Reorder the terms:
-5.2 + 5.2 + -7.2x + x2 = 0 + 5.2

Combine like terms: -5.2 + 5.2 = 0.0
0.0 + -7.2x + x2 = 0 + 5.2
-7.2x + x2 = 0 + 5.2

Combine like terms: 0 + 5.2 = 5.2
-7.2x + x2 = 5.2

The x term is -7.2x.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2x + 12.96 + x2 = 5.2 + 12.96

Reorder the terms:
12.96 + -7.2x + x2 = 5.2 + 12.96

Combine like terms: 5.2 + 12.96 = 18.16
12.96 + -7.2x + x2 = 18.16

Factor a perfect square on the left side:
(x + -3.6)(x + -3.6) = 18.16

Calculate the square root of the right side: 4.261455151

Break this problem into two subproblems by setting 
(x + -3.6) equal to 4.261455151 and -4.261455151.

Subproblem 1

x + -3.6 = 4.261455151 Simplifying x + -3.6 = 4.261455151 Reorder the terms: -3.6 + x = 4.261455151 Solving -3.6 + x = 4.261455151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 4.261455151 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 4.261455151 + 3.6 x = 4.261455151 + 3.6 Combine like terms: 4.261455151 + 3.6 = 7.861455151 x = 7.861455151 Simplifying x = 7.861455151

Subproblem 2

x + -3.6 = -4.261455151 Simplifying x + -3.6 = -4.261455151 Reorder the terms: -3.6 + x = -4.261455151 Solving -3.6 + x = -4.261455151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -4.261455151 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -4.261455151 + 3.6 x = -4.261455151 + 3.6 Combine like terms: -4.261455151 + 3.6 = -0.661455151 x = -0.661455151 Simplifying x = -0.661455151

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.861455151, -0.661455151}

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