6x^2=2x+14

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Solution for 6x^2=2x+14 equation:


Simplifying
6x2 = 2x + 14

Reorder the terms:
6x2 = 14 + 2x

Solving
6x2 = 14 + 2x

Solving for variable 'x'.

Reorder the terms:
-14 + -2x + 6x2 = 14 + 2x + -14 + -2x

Reorder the terms:
-14 + -2x + 6x2 = 14 + -14 + 2x + -2x

Combine like terms: 14 + -14 = 0
-14 + -2x + 6x2 = 0 + 2x + -2x
-14 + -2x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-14 + -2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -1x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-7 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -7 + -1x + 3x2 = 0 Solving -7 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -0.3333333333x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -0.3333333333x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -0.3333333333x + x2 = 0 + 2.333333333 -0.3333333333x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -0.3333333333x + x2 = 2.333333333 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 2.333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 2.333333333 + 0.02777777779 Combine like terms: 2.333333333 + 0.02777777779 = 2.36111111079 0.02777777779 + -0.3333333333x + x2 = 2.36111111079 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 2.36111111079 Calculate the square root of the right side: 1.536590743 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 1.536590743 and -1.536590743.

Subproblem 1

x + -0.1666666667 = 1.536590743 Simplifying x + -0.1666666667 = 1.536590743 Reorder the terms: -0.1666666667 + x = 1.536590743 Solving -0.1666666667 + x = 1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 1.536590743 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.536590743 + 0.1666666667 x = 1.536590743 + 0.1666666667 Combine like terms: 1.536590743 + 0.1666666667 = 1.7032574097 x = 1.7032574097 Simplifying x = 1.7032574097

Subproblem 2

x + -0.1666666667 = -1.536590743 Simplifying x + -0.1666666667 = -1.536590743 Reorder the terms: -0.1666666667 + x = -1.536590743 Solving -0.1666666667 + x = -1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -1.536590743 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.536590743 + 0.1666666667 x = -1.536590743 + 0.1666666667 Combine like terms: -1.536590743 + 0.1666666667 = -1.3699240763 x = -1.3699240763 Simplifying x = -1.3699240763

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7032574097, -1.3699240763}

Solution

x = {1.7032574097, -1.3699240763}

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