tristatefabricatorsinc
Junior Member
- Joined
- Jan 31, 2006
- Messages
- 60
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}
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}