3x^2+14x=728

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Solution for 3x^2+14x=728 equation:


Simplifying
3x2 + 14x = 728

Reorder the terms:
14x + 3x2 = 728

Solving
14x + 3x2 = 728

Solving for variable 'x'.

Reorder the terms:
-728 + 14x + 3x2 = 728 + -728

Combine like terms: 728 + -728 = 0
-728 + 14x + 3x2 = 0

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

Divide each side by '3'.
-242.6666667 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '242.6666667' to each side of the equation.
-242.6666667 + 4.666666667x + 242.6666667 + x2 = 0 + 242.6666667

Reorder the terms:
-242.6666667 + 242.6666667 + 4.666666667x + x2 = 0 + 242.6666667

Combine like terms: -242.6666667 + 242.6666667 = 0.0000000
0.0000000 + 4.666666667x + x2 = 0 + 242.6666667
4.666666667x + x2 = 0 + 242.6666667

Combine like terms: 0 + 242.6666667 = 242.6666667
4.666666667x + x2 = 242.6666667

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 = 242.6666667 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 242.6666667 + 5.444444448

Combine like terms: 242.6666667 + 5.444444448 = 248.111111148
5.444444448 + 4.666666667x + x2 = 248.111111148

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 248.111111148

Calculate the square root of the right side: 15.751543135

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 15.751543135 and -15.751543135.

Subproblem 1

x + 2.333333334 = 15.751543135 Simplifying x + 2.333333334 = 15.751543135 Reorder the terms: 2.333333334 + x = 15.751543135 Solving 2.333333334 + x = 15.751543135 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 = 15.751543135 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 15.751543135 + -2.333333334 x = 15.751543135 + -2.333333334 Combine like terms: 15.751543135 + -2.333333334 = 13.418209801 x = 13.418209801 Simplifying x = 13.418209801

Subproblem 2

x + 2.333333334 = -15.751543135 Simplifying x + 2.333333334 = -15.751543135 Reorder the terms: 2.333333334 + x = -15.751543135 Solving 2.333333334 + x = -15.751543135 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 = -15.751543135 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -15.751543135 + -2.333333334 x = -15.751543135 + -2.333333334 Combine like terms: -15.751543135 + -2.333333334 = -18.084876469 x = -18.084876469 Simplifying x = -18.084876469

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.418209801, -18.084876469}

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