3x(x+3)=-5

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


Simplifying
3x(x + 3) = -5

Reorder the terms:
3x(3 + x) = -5
(3 * 3x + x * 3x) = -5
(9x + 3x2) = -5

Solving
9x + 3x2 = -5

Solving for variable 'x'.

Reorder the terms:
5 + 9x + 3x2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 9x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + 3x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 3x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 3x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 3x + x2 = 0 + -1.666666667
3x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
3x + x2 = -1.666666667

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 = -1.666666667 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -1.666666667 + 2.25

Combine like terms: -1.666666667 + 2.25 = 0.583333333
2.25 + 3x + x2 = 0.583333333

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 0.583333333

Calculate the square root of the right side: 0.763762616

Break this problem into two subproblems by setting 
(x + 1.5) equal to 0.763762616 and -0.763762616.

Subproblem 1

x + 1.5 = 0.763762616 Simplifying x + 1.5 = 0.763762616 Reorder the terms: 1.5 + x = 0.763762616 Solving 1.5 + x = 0.763762616 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 = 0.763762616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.763762616 + -1.5 x = 0.763762616 + -1.5 Combine like terms: 0.763762616 + -1.5 = -0.736237384 x = -0.736237384 Simplifying x = -0.736237384

Subproblem 2

x + 1.5 = -0.763762616 Simplifying x + 1.5 = -0.763762616 Reorder the terms: 1.5 + x = -0.763762616 Solving 1.5 + x = -0.763762616 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 = -0.763762616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.763762616 + -1.5 x = -0.763762616 + -1.5 Combine like terms: -0.763762616 + -1.5 = -2.263762616 x = -2.263762616 Simplifying x = -2.263762616

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.736237384, -2.263762616}

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