Completing the Square: 3x^3 - 6x - 24 = 0

Can someone tell me where I have made an error in my problem?

Quadratic Equation #1 -
Solving Quadratic Equation by Completing the Square

Original Problem: 3x^2 - 6x - 24 = 0

Solving
3x^2 -6x -24 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(x^2 - 2x – 8) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(x^2 - 2x – 8)' equal to zero and attempt to solve:

Solving
x^2 - 2x – 8 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
x^2 - 2x – 8 + 8 = 0 + 8

Combine like terms: -8 + 8 = 0
x^2 - 2x + 0 = 8
x^2 - 2x = 0 + 8

Combine like terms: 0 + 8 = 8
x^2 - 2x = 8

The x term is -2 xs. Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
x^2 - 2x + 1 = 8 + 1

Combine like terms: 8 + 1 = 9
x^2 - 2x + 1 = 9

Factor a perfect square on the left side:
(x + -1)(x + -1) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting
(x + -1) equal to 3 and -3.

Subproblem 2

Solving
-1 + x = 3

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = 3 + 1

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

Combine like terms: 3 + 1 = 4
x = 4

Simplifying
x = 4
Subproblem 3

Solving
-1 + x = -3

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = -3 + 1

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

Combine like terms: -3 + 1 = -2
x = -2

Simplifying
x = -2
Solution
x = {4, -2}

Sorry to disappoint you, but I don't see any mistakes. Don't forget that you should always check your answers in the original equation to see if they give a true statement.

Steve

Thank you, my professor was telling me I had an error and I could not find it. I thought I was correct.

Your methodology looks spot-on, and your solution checks:

. . .3x² - 6x - 24 = 0, with x = -2:

. . .3(-2)² - 6(-2) - 24
. . . . .= 3(4) + 12 - 24
. . . . .= 12 + 12 - 24
. . . . .= 24 - 24
. . . . .= 0

. . .3x² - 6x - 24 = 0, with x = 4:

. . .3(4)² - 6(4) - 24
. . . . .= 3(16) - 24 - 24
. . . . .= 48 - 24 - 24
. . . . .= 48 - 48
. . . . .= 0

I agree with you.

Eliz.

Re: Completing the Square

tristatefabricatorsinc said:

3x^2 -6x -24 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(x^2 - 2x – 8) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(x^2 - 2x – 8)' equal to zero and attempt to solve:

Solving
x^2 - 2x – 8 = 0

Click to expand...

WHO the heck is forcing you to do ALL that typing; your teacher?

3x^2 - 6x - 24 = 0
Solving for variable 'x':

Divide by GCF 3:
x^2 - 2x - 8 = 0

Like, that's all you need for that portion...