Jedida solved the quadratic equation x2−96=4x
by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?
x2−96=4x
Step 1: x2+4x−96=0
Add 4x
to both sides.
Step 2: (x+12)(x−8)=0
Factor.
Step 3: x+12=0
or x−8=0
Use the Zero Product Property.
x=−12
or x=8
Jedida did not make any mistakes in solving the quadratic equation.
Based on the given information, Jedida did not make any mistakes during the factoring process. All the steps she followed are correct.
Jedida made a mistake at Step 2.
To solve the quadratic equation x^2 - 96 = 4x by factoring, we need to rearrange the equation to have the variable terms on one side and the constant term on the other side. Here is the correct step-by-step process:
Step 1: x^2 - 4x - 96 = 0
Add 4x to both sides to move the variable terms to the left side of the equation.
Step 2: x^2 - 4x = 96
The equation is now in the form ax^2 + bx + c = 0, where a = 1, b = -4, and c = 96.
Step 3: We need to find two numbers that multiply to give ac (1 * 96 = 96) and add up to give b (-4). In this case, the numbers are -12 and 8 since -12 * 8 = 96 and -12 + 8 = -4.
Step 4: Rewrite the equation using these two numbers: x^2 - 12x + 8x - 96 = 0
Note: We divide the b term (-4x) into two terms, -12x and +8x.
Step 5: Group the terms: (x^2 - 12x) + (8x - 96) = 0
Step 6: Factor by grouping: x(x - 12) + 8(x - 12) = 0
Step 7: Combine like terms: (x + 8)(x - 12) = 0
Step 8: Apply the Zero Product Property: x + 8 = 0 or x - 12 = 0
Step 9: Solve for x: x = -8 or x = 12
Therefore, Jedida made a mistake at Step 2 where she incorrectly factored the equation. It should be (x + 8)(x - 12) = 0 instead of (x + 12)(x - 8) = 0.