3x+3x^2=88

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Solution for 3x+3x^2=88 equation:


Simplifying
3x + 3x2 = 88

Solving
3x + 3x2 = 88

Solving for variable 'x'.

Reorder the terms:
-88 + 3x + 3x2 = 88 + -88

Combine like terms: 88 + -88 = 0
-88 + 3x + 3x2 = 0

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

Divide each side by '3'.
-29.33333333 + x + x2 = 0

Move the constant term to the right:

Add '29.33333333' to each side of the equation.
-29.33333333 + x + 29.33333333 + x2 = 0 + 29.33333333

Reorder the terms:
-29.33333333 + 29.33333333 + x + x2 = 0 + 29.33333333

Combine like terms: -29.33333333 + 29.33333333 = 0.00000000
0.00000000 + x + x2 = 0 + 29.33333333
x + x2 = 0 + 29.33333333

Combine like terms: 0 + 29.33333333 = 29.33333333
x + x2 = 29.33333333

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 = 29.33333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 29.33333333 + 0.25

Combine like terms: 29.33333333 + 0.25 = 29.58333333
1.25 + x2 = 29.58333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 29.58333333

Calculate the square root of the right side: 5.43905629

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.43905629 and -5.43905629.

Subproblem 1

x + 0.5 = 5.43905629 Simplifying x + 0.5 = 5.43905629 Reorder the terms: 0.5 + x = 5.43905629 Solving 0.5 + x = 5.43905629 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 = 5.43905629 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.43905629 + -0.5 x = 5.43905629 + -0.5 Combine like terms: 5.43905629 + -0.5 = 4.93905629 x = 4.93905629 Simplifying x = 4.93905629

Subproblem 2

x + 0.5 = -5.43905629 Simplifying x + 0.5 = -5.43905629 Reorder the terms: 0.5 + x = -5.43905629 Solving 0.5 + x = -5.43905629 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 = -5.43905629 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.43905629 + -0.5 x = -5.43905629 + -0.5 Combine like terms: -5.43905629 + -0.5 = -5.93905629 x = -5.93905629 Simplifying x = -5.93905629

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.93905629, -5.93905629}

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