6x^2+16x+2=

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Solution for 6x^2+16x+2= equation:


Simplifying
6x2 + 16x + 2 = 0

Reorder the terms:
2 + 16x + 6x2 = 0

Solving
2 + 16x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 8x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + 8x + 3x2 = 0 Solving 1 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 2.666666667x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 2.666666667x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 2.666666667x + x2 = 0 + -0.3333333333 2.666666667x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 2.666666667x + x2 = -0.3333333333 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -0.3333333333 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -0.3333333333 + 1.777777780 Combine like terms: -0.3333333333 + 1.777777780 = 1.4444444467 1.777777780 + 2.666666667x + x2 = 1.4444444467 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 1.4444444467 Calculate the square root of the right side: 1.201850426 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.201850426 and -1.201850426.

Subproblem 1

x + 1.333333334 = 1.201850426 Simplifying x + 1.333333334 = 1.201850426 Reorder the terms: 1.333333334 + x = 1.201850426 Solving 1.333333334 + x = 1.201850426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 1.201850426 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.201850426 + -1.333333334 x = 1.201850426 + -1.333333334 Combine like terms: 1.201850426 + -1.333333334 = -0.131482908 x = -0.131482908 Simplifying x = -0.131482908

Subproblem 2

x + 1.333333334 = -1.201850426 Simplifying x + 1.333333334 = -1.201850426 Reorder the terms: 1.333333334 + x = -1.201850426 Solving 1.333333334 + x = -1.201850426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -1.201850426 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.201850426 + -1.333333334 x = -1.201850426 + -1.333333334 Combine like terms: -1.201850426 + -1.333333334 = -2.53518376 x = -2.53518376 Simplifying x = -2.53518376

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.131482908, -2.53518376}

Solution

x = {-0.131482908, -2.53518376}

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