3x^2-14x=-1

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Solution for 3x^2-14x=-1 equation:


Simplifying
3x2 + -14x = -1

Reorder the terms:
-14x + 3x2 = -1

Solving
-14x + 3x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + -14x + 3x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -14x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
0.3333333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -4.666666667x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -4.666666667x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -4.666666667x + x2 = 0 + -0.3333333333
-4.666666667x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-4.666666667x + x2 = -0.3333333333

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = -0.3333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = -0.3333333333 + 5.444444448

Combine like terms: -0.3333333333 + 5.444444448 = 5.1111111147
5.444444448 + -4.666666667x + x2 = 5.1111111147

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 5.1111111147

Calculate the square root of the right side: 2.260776662

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.260776662 and -2.260776662.

Subproblem 1

x + -2.333333334 = 2.260776662 Simplifying x + -2.333333334 = 2.260776662 Reorder the terms: -2.333333334 + x = 2.260776662 Solving -2.333333334 + x = 2.260776662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 2.260776662 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 2.260776662 + 2.333333334 x = 2.260776662 + 2.333333334 Combine like terms: 2.260776662 + 2.333333334 = 4.594109996 x = 4.594109996 Simplifying x = 4.594109996

Subproblem 2

x + -2.333333334 = -2.260776662 Simplifying x + -2.333333334 = -2.260776662 Reorder the terms: -2.333333334 + x = -2.260776662 Solving -2.333333334 + x = -2.260776662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -2.260776662 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -2.260776662 + 2.333333334 x = -2.260776662 + 2.333333334 Combine like terms: -2.260776662 + 2.333333334 = 0.072556672 x = 0.072556672 Simplifying x = 0.072556672

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.594109996, 0.072556672}

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