3x^2+4x=18

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Solution for 3x^2+4x=18 equation:


Simplifying
3x2 + 4x = 18

Reorder the terms:
4x + 3x2 = 18

Solving
4x + 3x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 4x + 3x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 4x + 3x2 = 0

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

Divide each side by '3'.
-6 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 1.333333333x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 1.333333333x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 1.333333333x + x2 = 0 + 6
1.333333333x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
1.333333333x + x2 = 6

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 6 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 6 + 0.4444444442

Combine like terms: 6 + 0.4444444442 = 6.4444444442
0.4444444442 + 1.333333333x + x2 = 6.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 6.4444444442

Calculate the square root of the right side: 2.538591035

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 2.538591035 and -2.538591035.

Subproblem 1

x + 0.6666666665 = 2.538591035 Simplifying x + 0.6666666665 = 2.538591035 Reorder the terms: 0.6666666665 + x = 2.538591035 Solving 0.6666666665 + x = 2.538591035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 2.538591035 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 2.538591035 + -0.6666666665 x = 2.538591035 + -0.6666666665 Combine like terms: 2.538591035 + -0.6666666665 = 1.8719243685 x = 1.8719243685 Simplifying x = 1.8719243685

Subproblem 2

x + 0.6666666665 = -2.538591035 Simplifying x + 0.6666666665 = -2.538591035 Reorder the terms: 0.6666666665 + x = -2.538591035 Solving 0.6666666665 + x = -2.538591035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -2.538591035 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -2.538591035 + -0.6666666665 x = -2.538591035 + -0.6666666665 Combine like terms: -2.538591035 + -0.6666666665 = -3.2052577015 x = -3.2052577015 Simplifying x = -3.2052577015

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.8719243685, -3.2052577015}

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