Peta attempted to solve the following equation. Explain Peta's error.

x (x - 5) = 20
x = 20 and x - 5 = 20
x = 20 and x = 25

Peta can only use the zero product property when the product of factors is equal to zero.

Peta must multiply x by (x - 5).

Peta must write the equation in standard form, then factor the expression.

Each factor must be set equal to zero, not 20.

Peta needs to get tutoring from her brother in college.

She is setting the function
a*b=n and assuming a is equal to n or b is equal to n, that would only occur if the other factor is one, and there is no reason to believe that.

only in the instance of
ab=0 can one assume a is zero, or b is zero, or both are zero.

only in the instance of

ab=0 can one assume a is zero, or b is zero, or both are zero.

Peta can only use the zero product property when the product of factors is equal to zero.

Peta must multiply x by (x - 5).

Peta must write the equation in standard form, then factor the expression.

Each factor must be set equal to zero, not 20.

Peta's error in solving the equation x (x - 5) = 20 is that she incorrectly set up two separate equations and solved them independently.

Let's break down the correct approach to solving this equation:

1. Start with the given equation: x(x - 5) = 20.

2. Distribute the x on the left side of the equation: x^2 - 5x = 20.

3. Rearrange the equation to set it equal to zero: x^2 - 5x - 20 = 0.

4. To solve this quadratic equation, we can try factoring, completing the square, or using the quadratic formula. In this case, let's factor the quadratic equation:

(x - 8)(x + 3) = 0.

5. Set each factor equal to zero and solve for x:

x - 8 = 0 or x + 3 = 0.

Solving the first equation, we get: x = 8.
Solving the second equation, we get: x = -3.

So, the correct solutions to the equation x(x - 5) = 20 are x = 8 and x = -3.

Peta's error lies in incorrectly setting up two separate equations x = 20 and x - 5 = 20. This approach does not consider the relationship between the two factors in the equation x(x - 5) = 20. It is crucial to solve the equation as a whole instead of breaking it down into separate equations to obtain the correct solution.