3x^2+3x=8

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Solution for 3x^2+3x=8 equation:


Simplifying
3x2 + 3x = 8

Reorder the terms:
3x + 3x2 = 8

Solving
3x + 3x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 3x + 3x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 3x + 3x2 = 0

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

Divide each side by '3'.
-2.666666667 + x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x + x2 = 0 + 2.666666667
x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
x + x2 = 2.666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 2.666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 2.666666667 + 0.25

Combine like terms: 2.666666667 + 0.25 = 2.916666667
1.25 + x2 = 2.916666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.916666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.707825128 and -1.707825128.

Subproblem 1

x + 0.5 = 1.707825128 Simplifying x + 0.5 = 1.707825128 Reorder the terms: 0.5 + x = 1.707825128 Solving 0.5 + x = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.707825128 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.707825128 + -0.5 x = 1.707825128 + -0.5 Combine like terms: 1.707825128 + -0.5 = 1.207825128 x = 1.207825128 Simplifying x = 1.207825128

Subproblem 2

x + 0.5 = -1.707825128 Simplifying x + 0.5 = -1.707825128 Reorder the terms: 0.5 + x = -1.707825128 Solving 0.5 + x = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.707825128 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.707825128 + -0.5 x = -1.707825128 + -0.5 Combine like terms: -1.707825128 + -0.5 = -2.207825128 x = -2.207825128 Simplifying x = -2.207825128

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.207825128, -2.207825128}

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