6x^2-16x=49

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Solution for 6x^2-16x=49 equation:


Simplifying
6x2 + -16x = 49

Reorder the terms:
-16x + 6x2 = 49

Solving
-16x + 6x2 = 49

Solving for variable 'x'.

Reorder the terms:
-49 + -16x + 6x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + -16x + 6x2 = 0

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

Divide each side by '6'.
-8.166666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '8.166666667' to each side of the equation.
-8.166666667 + -2.666666667x + 8.166666667 + x2 = 0 + 8.166666667

Reorder the terms:
-8.166666667 + 8.166666667 + -2.666666667x + x2 = 0 + 8.166666667

Combine like terms: -8.166666667 + 8.166666667 = 0.000000000
0.000000000 + -2.666666667x + x2 = 0 + 8.166666667
-2.666666667x + x2 = 0 + 8.166666667

Combine like terms: 0 + 8.166666667 = 8.166666667
-2.666666667x + x2 = 8.166666667

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 = 8.166666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 8.166666667 + 1.777777780

Combine like terms: 8.166666667 + 1.777777780 = 9.944444447
1.777777780 + -2.666666667x + x2 = 9.944444447

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 9.944444447

Calculate the square root of the right side: 3.153481322

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 3.153481322 and -3.153481322.

Subproblem 1

x + -1.333333334 = 3.153481322 Simplifying x + -1.333333334 = 3.153481322 Reorder the terms: -1.333333334 + x = 3.153481322 Solving -1.333333334 + x = 3.153481322 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 = 3.153481322 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 3.153481322 + 1.333333334 x = 3.153481322 + 1.333333334 Combine like terms: 3.153481322 + 1.333333334 = 4.486814656 x = 4.486814656 Simplifying x = 4.486814656

Subproblem 2

x + -1.333333334 = -3.153481322 Simplifying x + -1.333333334 = -3.153481322 Reorder the terms: -1.333333334 + x = -3.153481322 Solving -1.333333334 + x = -3.153481322 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 = -3.153481322 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -3.153481322 + 1.333333334 x = -3.153481322 + 1.333333334 Combine like terms: -3.153481322 + 1.333333334 = -1.820147988 x = -1.820147988 Simplifying x = -1.820147988

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.486814656, -1.820147988}

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