x(x-9)=30

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Solution for x(x-9)=30 equation:


Simplifying
x(x + -9) = 30

Reorder the terms:
x(-9 + x) = 30
(-9 * x + x * x) = 30
(-9x + x2) = 30

Solving
-9x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + -9x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -9x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -9x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -9x + x2 = 0 + 30
-9x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-9x + x2 = 30

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 30 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 30 + 20.25

Combine like terms: 30 + 20.25 = 50.25
20.25 + -9x + x2 = 50.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(x + -4.5) equal to 7.088723439 and -7.088723439.

Subproblem 1

x + -4.5 = 7.088723439 Simplifying x + -4.5 = 7.088723439 Reorder the terms: -4.5 + x = 7.088723439 Solving -4.5 + x = 7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 7.088723439 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.088723439 + 4.5 x = 7.088723439 + 4.5 Combine like terms: 7.088723439 + 4.5 = 11.588723439 x = 11.588723439 Simplifying x = 11.588723439

Subproblem 2

x + -4.5 = -7.088723439 Simplifying x + -4.5 = -7.088723439 Reorder the terms: -4.5 + x = -7.088723439 Solving -4.5 + x = -7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -7.088723439 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.088723439 + 4.5 x = -7.088723439 + 4.5 Combine like terms: -7.088723439 + 4.5 = -2.588723439 x = -2.588723439 Simplifying x = -2.588723439

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.588723439, -2.588723439}

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