6x^2=2-14x

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


Simplifying
6x2 = 2 + -14x

Solving
6x2 = 2 + -14x

Solving for variable 'x'.

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

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

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

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

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + 7x + 3x2)' equal to zero and attempt to solve: Simplifying -1 + 7x + 3x2 = 0 Solving -1 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 2.333333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 2.333333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 2.333333333x + x2 = 0 + 0.3333333333 2.333333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 2.333333333x + x2 = 0.3333333333 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 0.3333333333 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 0.3333333333 + 1.361111112 Combine like terms: 0.3333333333 + 1.361111112 = 1.6944444453 1.361111112 + 2.333333333x + x2 = 1.6944444453 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 1.6944444453 Calculate the square root of the right side: 1.30170828 Break this problem into two subproblems by setting (x + 1.166666667) equal to 1.30170828 and -1.30170828.

Subproblem 1

x + 1.166666667 = 1.30170828 Simplifying x + 1.166666667 = 1.30170828 Reorder the terms: 1.166666667 + x = 1.30170828 Solving 1.166666667 + x = 1.30170828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 1.30170828 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 1.30170828 + -1.166666667 x = 1.30170828 + -1.166666667 Combine like terms: 1.30170828 + -1.166666667 = 0.135041613 x = 0.135041613 Simplifying x = 0.135041613

Subproblem 2

x + 1.166666667 = -1.30170828 Simplifying x + 1.166666667 = -1.30170828 Reorder the terms: 1.166666667 + x = -1.30170828 Solving 1.166666667 + x = -1.30170828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -1.30170828 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -1.30170828 + -1.166666667 x = -1.30170828 + -1.166666667 Combine like terms: -1.30170828 + -1.166666667 = -2.468374947 x = -2.468374947 Simplifying x = -2.468374947

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.135041613, -2.468374947}

Solution

x = {0.135041613, -2.468374947}

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