3x(x+4)=5

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Solution for 3x(x+4)=5 equation:


Simplifying
3x(x + 4) = 5

Reorder the terms:
3x(4 + x) = 5
(4 * 3x + x * 3x) = 5
(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 = 5.666666667
4 + 4x + x2 = 5.666666667

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5.666666667

Calculate the square root of the right side: 2.380476143

Break this problem into two subproblems by setting 
(x + 2) equal to 2.380476143 and -2.380476143.

Subproblem 1

x + 2 = 2.380476143 Simplifying x + 2 = 2.380476143 Reorder the terms: 2 + x = 2.380476143 Solving 2 + x = 2.380476143 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 = 2.380476143 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.380476143 + -2 x = 2.380476143 + -2 Combine like terms: 2.380476143 + -2 = 0.380476143 x = 0.380476143 Simplifying x = 0.380476143

Subproblem 2

x + 2 = -2.380476143 Simplifying x + 2 = -2.380476143 Reorder the terms: 2 + x = -2.380476143 Solving 2 + x = -2.380476143 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 = -2.380476143 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.380476143 + -2 x = -2.380476143 + -2 Combine like terms: -2.380476143 + -2 = -4.380476143 x = -4.380476143 Simplifying x = -4.380476143

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.380476143, -4.380476143}

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