x(x+3)=330

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Solution for x(x+3)=330 equation:


Simplifying
x(x + 3) = 330

Reorder the terms:
x(3 + x) = 330
(3 * x + x * x) = 330
(3x + x2) = 330

Solving
3x + x2 = 330

Solving for variable 'x'.

Reorder the terms:
-330 + 3x + x2 = 330 + -330

Combine like terms: 330 + -330 = 0
-330 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '330' to each side of the equation.
-330 + 3x + 330 + x2 = 0 + 330

Reorder the terms:
-330 + 330 + 3x + x2 = 0 + 330

Combine like terms: -330 + 330 = 0
0 + 3x + x2 = 0 + 330
3x + x2 = 0 + 330

Combine like terms: 0 + 330 = 330
3x + x2 = 330

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 330 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 330 + 2.25

Combine like terms: 330 + 2.25 = 332.25
2.25 + 3x + x2 = 332.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 332.25

Calculate the square root of the right side: 18.227726134

Break this problem into two subproblems by setting 
(x + 1.5) equal to 18.227726134 and -18.227726134.

Subproblem 1

x + 1.5 = 18.227726134 Simplifying x + 1.5 = 18.227726134 Reorder the terms: 1.5 + x = 18.227726134 Solving 1.5 + x = 18.227726134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 18.227726134 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 18.227726134 + -1.5 x = 18.227726134 + -1.5 Combine like terms: 18.227726134 + -1.5 = 16.727726134 x = 16.727726134 Simplifying x = 16.727726134

Subproblem 2

x + 1.5 = -18.227726134 Simplifying x + 1.5 = -18.227726134 Reorder the terms: 1.5 + x = -18.227726134 Solving 1.5 + x = -18.227726134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -18.227726134 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -18.227726134 + -1.5 x = -18.227726134 + -1.5 Combine like terms: -18.227726134 + -1.5 = -19.727726134 x = -19.727726134 Simplifying x = -19.727726134

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.727726134, -19.727726134}

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