5x(x+9)-5=45-33

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Solution for 5x(x+9)-5=45-33 equation:


Simplifying
5x(x + 9) + -5 = 45 + -33

Reorder the terms:
5x(9 + x) + -5 = 45 + -33
(9 * 5x + x * 5x) + -5 = 45 + -33
(45x + 5x2) + -5 = 45 + -33

Reorder the terms:
-5 + 45x + 5x2 = 45 + -33

Combine like terms: 45 + -33 = 12
-5 + 45x + 5x2 = 12

Solving
-5 + 45x + 5x2 = 12

Solving for variable 'x'.

Reorder the terms:
-5 + -12 + 45x + 5x2 = 12 + -12

Combine like terms: -5 + -12 = -17
-17 + 45x + 5x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-17 + 45x + 5x2 = 0

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

Divide each side by '5'.
-3.4 + 9x + x2 = 0

Move the constant term to the right:

Add '3.4' to each side of the equation.
-3.4 + 9x + 3.4 + x2 = 0 + 3.4

Reorder the terms:
-3.4 + 3.4 + 9x + x2 = 0 + 3.4

Combine like terms: -3.4 + 3.4 = 0.0
0.0 + 9x + x2 = 0 + 3.4
9x + x2 = 0 + 3.4

Combine like terms: 0 + 3.4 = 3.4
9x + x2 = 3.4

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 = 3.4 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 3.4 + 20.25

Combine like terms: 3.4 + 20.25 = 23.65
20.25 + 9x + x2 = 23.65

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 23.65

Calculate the square root of the right side: 4.863126566

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.863126566 and -4.863126566.

Subproblem 1

x + 4.5 = 4.863126566 Simplifying x + 4.5 = 4.863126566 Reorder the terms: 4.5 + x = 4.863126566 Solving 4.5 + x = 4.863126566 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 = 4.863126566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.863126566 + -4.5 x = 4.863126566 + -4.5 Combine like terms: 4.863126566 + -4.5 = 0.363126566 x = 0.363126566 Simplifying x = 0.363126566

Subproblem 2

x + 4.5 = -4.863126566 Simplifying x + 4.5 = -4.863126566 Reorder the terms: 4.5 + x = -4.863126566 Solving 4.5 + x = -4.863126566 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 = -4.863126566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.863126566 + -4.5 x = -4.863126566 + -4.5 Combine like terms: -4.863126566 + -4.5 = -9.363126566 x = -9.363126566 Simplifying x = -9.363126566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.363126566, -9.363126566}

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