5(x+3)x=3

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Solution for 5(x+3)x=3 equation:


Simplifying
5(x + 3) * x = 3

Reorder the terms:
5(3 + x) * x = 3

Reorder the terms for easier multiplication:
5x(3 + x) = 3
(3 * 5x + x * 5x) = 3
(15x + 5x2) = 3

Solving
15x + 5x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 15x + 5x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 15x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + 3x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 3x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 3x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 3x + x2 = 0 + 0.6
3x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
3x + x2 = 0.6

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 = 0.6 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.6 + 2.25

Combine like terms: 0.6 + 2.25 = 2.85
2.25 + 3x + x2 = 2.85

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.85

Calculate the square root of the right side: 1.688194302

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.688194302 and -1.688194302.

Subproblem 1

x + 1.5 = 1.688194302 Simplifying x + 1.5 = 1.688194302 Reorder the terms: 1.5 + x = 1.688194302 Solving 1.5 + x = 1.688194302 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 = 1.688194302 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.688194302 + -1.5 x = 1.688194302 + -1.5 Combine like terms: 1.688194302 + -1.5 = 0.188194302 x = 0.188194302 Simplifying x = 0.188194302

Subproblem 2

x + 1.5 = -1.688194302 Simplifying x + 1.5 = -1.688194302 Reorder the terms: 1.5 + x = -1.688194302 Solving 1.5 + x = -1.688194302 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 = -1.688194302 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.688194302 + -1.5 x = -1.688194302 + -1.5 Combine like terms: -1.688194302 + -1.5 = -3.188194302 x = -3.188194302 Simplifying x = -3.188194302

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.188194302, -3.188194302}

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