3x*x+32x+15=0

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Solution for 3x*x+32x+15=0 equation:


Simplifying
3x * x + 32x + 15 = 0

Multiply x * x
3x2 + 32x + 15 = 0

Reorder the terms:
15 + 32x + 3x2 = 0

Solving
15 + 32x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
5 + 10.66666667x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 10.66666667x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 10.66666667x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 10.66666667x + x2 = 0 + -5
10.66666667x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
10.66666667x + x2 = -5

The x term is 10.66666667x.  Take half its coefficient (5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
10.66666667x + 28.44444446 + x2 = -5 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667x + x2 = -5 + 28.44444446

Combine like terms: -5 + 28.44444446 = 23.44444446
28.44444446 + 10.66666667x + x2 = 23.44444446

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = 23.44444446

Calculate the square root of the right side: 4.84194635

Break this problem into two subproblems by setting 
(x + 5.333333335) equal to 4.84194635 and -4.84194635.

Subproblem 1

x + 5.333333335 = 4.84194635 Simplifying x + 5.333333335 = 4.84194635 Reorder the terms: 5.333333335 + x = 4.84194635 Solving 5.333333335 + x = 4.84194635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 4.84194635 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 4.84194635 + -5.333333335 x = 4.84194635 + -5.333333335 Combine like terms: 4.84194635 + -5.333333335 = -0.491386985 x = -0.491386985 Simplifying x = -0.491386985

Subproblem 2

x + 5.333333335 = -4.84194635 Simplifying x + 5.333333335 = -4.84194635 Reorder the terms: 5.333333335 + x = -4.84194635 Solving 5.333333335 + x = -4.84194635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -4.84194635 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -4.84194635 + -5.333333335 x = -4.84194635 + -5.333333335 Combine like terms: -4.84194635 + -5.333333335 = -10.175279685 x = -10.175279685 Simplifying x = -10.175279685

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.491386985, -10.175279685}

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