6x^2+2(11x-2)=0

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Solution for 6x^2+2(11x-2)=0 equation:


Simplifying
6x2 + 2(11x + -2) = 0

Reorder the terms:
6x2 + 2(-2 + 11x) = 0
6x2 + (-2 * 2 + 11x * 2) = 0
6x2 + (-4 + 22x) = 0

Reorder the terms:
-4 + 22x + 6x2 = 0

Solving
-4 + 22x + 6x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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 = 4.0277777807 3.361111114 + 3.666666667x + x2 = 4.0277777807 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 4.0277777807 Calculate the square root of the right side: 2.006932431 Break this problem into two subproblems by setting (x + 1.833333334) equal to 2.006932431 and -2.006932431.

Subproblem 1

x + 1.833333334 = 2.006932431 Simplifying x + 1.833333334 = 2.006932431 Reorder the terms: 1.833333334 + x = 2.006932431 Solving 1.833333334 + x = 2.006932431 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 = 2.006932431 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 2.006932431 + -1.833333334 x = 2.006932431 + -1.833333334 Combine like terms: 2.006932431 + -1.833333334 = 0.173599097 x = 0.173599097 Simplifying x = 0.173599097

Subproblem 2

x + 1.833333334 = -2.006932431 Simplifying x + 1.833333334 = -2.006932431 Reorder the terms: 1.833333334 + x = -2.006932431 Solving 1.833333334 + x = -2.006932431 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 = -2.006932431 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -2.006932431 + -1.833333334 x = -2.006932431 + -1.833333334 Combine like terms: -2.006932431 + -1.833333334 = -3.840265765 x = -3.840265765 Simplifying x = -3.840265765

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.173599097, -3.840265765}

Solution

x = {0.173599097, -3.840265765}

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