(x+3)x=30

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Solution for (x+3)x=30 equation:


Simplifying
(x + 3) * x = 30

Reorder the terms:
(3 + x) * x = 30

Reorder the terms for easier multiplication:
x(3 + x) = 30
(3 * x + x * x) = 30
(3x + x2) = 30

Solving
3x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 3x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 3x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 3x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 3x + x2 = 0 + 30
3x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
3x + x2 = 30

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 = 30 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 30 + 2.25

Combine like terms: 30 + 2.25 = 32.25
2.25 + 3x + x2 = 32.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 1.5) equal to 5.678908346 and -5.678908346.

Subproblem 1

x + 1.5 = 5.678908346 Simplifying x + 1.5 = 5.678908346 Reorder the terms: 1.5 + x = 5.678908346 Solving 1.5 + x = 5.678908346 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 = 5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.678908346 + -1.5 x = 5.678908346 + -1.5 Combine like terms: 5.678908346 + -1.5 = 4.178908346 x = 4.178908346 Simplifying x = 4.178908346

Subproblem 2

x + 1.5 = -5.678908346 Simplifying x + 1.5 = -5.678908346 Reorder the terms: 1.5 + x = -5.678908346 Solving 1.5 + x = -5.678908346 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 = -5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.678908346 + -1.5 x = -5.678908346 + -1.5 Combine like terms: -5.678908346 + -1.5 = -7.178908346 x = -7.178908346 Simplifying x = -7.178908346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.178908346, -7.178908346}

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