3x^2+2x+1=56

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Solution for 3x^2+2x+1=56 equation:


Simplifying
3x2 + 2x + 1 = 56

Reorder the terms:
1 + 2x + 3x2 = 56

Solving
1 + 2x + 3x2 = 56

Solving for variable 'x'.

Reorder the terms:
1 + -56 + 2x + 3x2 = 56 + -56

Combine like terms: 1 + -56 = -55
-55 + 2x + 3x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-55 + 2x + 3x2 = 0

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

Divide each side by '3'.
-18.33333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '18.33333333' to each side of the equation.
-18.33333333 + 0.6666666667x + 18.33333333 + x2 = 0 + 18.33333333

Reorder the terms:
-18.33333333 + 18.33333333 + 0.6666666667x + x2 = 0 + 18.33333333

Combine like terms: -18.33333333 + 18.33333333 = 0.00000000
0.00000000 + 0.6666666667x + x2 = 0 + 18.33333333
0.6666666667x + x2 = 0 + 18.33333333

Combine like terms: 0 + 18.33333333 = 18.33333333
0.6666666667x + x2 = 18.33333333

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 18.33333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 18.33333333 + 0.1111111112

Combine like terms: 18.33333333 + 0.1111111112 = 18.4444444412
0.1111111112 + 0.6666666667x + x2 = 18.4444444412

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 18.4444444412

Calculate the square root of the right side: 4.294699575

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 4.294699575 and -4.294699575.

Subproblem 1

x + 0.3333333334 = 4.294699575 Simplifying x + 0.3333333334 = 4.294699575 Reorder the terms: 0.3333333334 + x = 4.294699575 Solving 0.3333333334 + x = 4.294699575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 4.294699575 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 4.294699575 + -0.3333333334 x = 4.294699575 + -0.3333333334 Combine like terms: 4.294699575 + -0.3333333334 = 3.9613662416 x = 3.9613662416 Simplifying x = 3.9613662416

Subproblem 2

x + 0.3333333334 = -4.294699575 Simplifying x + 0.3333333334 = -4.294699575 Reorder the terms: 0.3333333334 + x = -4.294699575 Solving 0.3333333334 + x = -4.294699575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -4.294699575 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -4.294699575 + -0.3333333334 x = -4.294699575 + -0.3333333334 Combine like terms: -4.294699575 + -0.3333333334 = -4.6280329084 x = -4.6280329084 Simplifying x = -4.6280329084

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.9613662416, -4.6280329084}

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