3x^2+12x=-5

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Solution for 3x^2+12x=-5 equation:


Simplifying
3x2 + 12x = -5

Reorder the terms:
12x + 3x2 = -5

Solving
12x + 3x2 = -5

Solving for variable 'x'.

Reorder the terms:
5 + 12x + 3x2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 12x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + 4x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 4x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 4x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 4x + x2 = 0 + -1.666666667
4x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
4x + x2 = -1.666666667

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -1.666666667 + 4

Reorder the terms:
4 + 4x + x2 = -1.666666667 + 4

Combine like terms: -1.666666667 + 4 = 2.333333333
4 + 4x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + 2) equal to 1.527525232 and -1.527525232.

Subproblem 1

x + 2 = 1.527525232 Simplifying x + 2 = 1.527525232 Reorder the terms: 2 + x = 1.527525232 Solving 2 + x = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.527525232 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.527525232 + -2 x = 1.527525232 + -2 Combine like terms: 1.527525232 + -2 = -0.472474768 x = -0.472474768 Simplifying x = -0.472474768

Subproblem 2

x + 2 = -1.527525232 Simplifying x + 2 = -1.527525232 Reorder the terms: 2 + x = -1.527525232 Solving 2 + x = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.527525232 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.527525232 + -2 x = -1.527525232 + -2 Combine like terms: -1.527525232 + -2 = -3.527525232 x = -3.527525232 Simplifying x = -3.527525232

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.472474768, -3.527525232}

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