3x^2-8x=24

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Solution for 3x^2-8x=24 equation:


Simplifying
3x2 + -8x = 24

Reorder the terms:
-8x + 3x2 = 24

Solving
-8x + 3x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -8x + 3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -8x + 3x2 = 0

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

Divide each side by '3'.
-8 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -2.666666667x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -2.666666667x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -2.666666667x + x2 = 0 + 8
-2.666666667x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-2.666666667x + x2 = 8

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 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 8 + 1.777777780

Combine like terms: 8 + 1.777777780 = 9.77777778
1.777777780 + -2.666666667x + x2 = 9.77777778

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 9.77777778

Calculate the square root of the right side: 3.12694384

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 3.12694384 and -3.12694384.

Subproblem 1

x + -1.333333334 = 3.12694384 Simplifying x + -1.333333334 = 3.12694384 Reorder the terms: -1.333333334 + x = 3.12694384 Solving -1.333333334 + x = 3.12694384 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 = 3.12694384 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 3.12694384 + 1.333333334 x = 3.12694384 + 1.333333334 Combine like terms: 3.12694384 + 1.333333334 = 4.460277174 x = 4.460277174 Simplifying x = 4.460277174

Subproblem 2

x + -1.333333334 = -3.12694384 Simplifying x + -1.333333334 = -3.12694384 Reorder the terms: -1.333333334 + x = -3.12694384 Solving -1.333333334 + x = -3.12694384 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 = -3.12694384 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -3.12694384 + 1.333333334 x = -3.12694384 + 1.333333334 Combine like terms: -3.12694384 + 1.333333334 = -1.793610506 x = -1.793610506 Simplifying x = -1.793610506

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.460277174, -1.793610506}

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