0=3x^2+11x+2

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Solution for 0=3x^2+11x+2 equation:


Simplifying
0 = 3x2 + 11x + 2

Reorder the terms:
0 = 2 + 11x + 3x2

Solving
0 = 2 + 11x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -2 = -2
-2 + -11x + -3x2 = 2 + 11x + 3x2 + -2 + -11x + -3x2

Reorder the terms:
-2 + -11x + -3x2 = 2 + -2 + 11x + -11x + 3x2 + -3x2

Combine like terms: 2 + -2 = 0
-2 + -11x + -3x2 = 0 + 11x + -11x + 3x2 + -3x2
-2 + -11x + -3x2 = 11x + -11x + 3x2 + -3x2

Combine like terms: 11x + -11x = 0
-2 + -11x + -3x2 = 0 + 3x2 + -3x2
-2 + -11x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-2 + -11x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 11x + 3x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(2 + 11x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + 11x + 3x2 = 0 Solving 2 + 11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 3.666666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 3.666666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 3.666666667x + x2 = 0 + -0.6666666667 3.666666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 3.666666667x + x2 = -0.6666666667 The x term is 3.666666667x. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667x + 3.361111114 + x2 = -0.6666666667 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = -0.6666666667 + 3.361111114 Combine like terms: -0.6666666667 + 3.361111114 = 2.6944444473 3.361111114 + 3.666666667x + x2 = 2.6944444473 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 2.6944444473 Calculate the square root of the right side: 1.641476301 Break this problem into two subproblems by setting (x + 1.833333334) equal to 1.641476301 and -1.641476301.

Subproblem 1

x + 1.833333334 = 1.641476301 Simplifying x + 1.833333334 = 1.641476301 Reorder the terms: 1.833333334 + x = 1.641476301 Solving 1.833333334 + x = 1.641476301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = 1.641476301 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 1.641476301 + -1.833333334 x = 1.641476301 + -1.833333334 Combine like terms: 1.641476301 + -1.833333334 = -0.191857033 x = -0.191857033 Simplifying x = -0.191857033

Subproblem 2

x + 1.833333334 = -1.641476301 Simplifying x + 1.833333334 = -1.641476301 Reorder the terms: 1.833333334 + x = -1.641476301 Solving 1.833333334 + x = -1.641476301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = -1.641476301 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -1.641476301 + -1.833333334 x = -1.641476301 + -1.833333334 Combine like terms: -1.641476301 + -1.833333334 = -3.474809635 x = -3.474809635 Simplifying x = -3.474809635

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.191857033, -3.474809635}

Solution

x = {-0.191857033, -3.474809635}

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