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 (1 point) Responses
Step 1; she added 4x to both sides instead of subtracting.
Step 3; she did not apply the Zero Product Property correctly.
She did not make any mistakes.
Step 2; she did not factor the left side of the equation correctly.
The mistake was made in Step 1. Jedida should have subtracted 4x from both sides instead of adding 4x.
Solve the following quadratic equation using the perfect square trinomial pattern: x2+x+0.25=0 .(1 point) Responses
x=0.25
x=−0.25
x=−0.5
x=0.5
To solve the quadratic equation using the perfect square trinomial pattern, we need to recognize that the equation is in the form of (x + a)^2 = 0.
In this case, we have x^2 + x + 0.25 = 0. To get the perfect square trinomial, we take half of the coefficient of x (which is 1) and square it.
Half of 1 is 0.5, and when we square it, we get 0.25.
So, we can write the equation as (x + 0.5)^2 = 0.
To solve this equation, we set the squared term equal to 0: x + 0.5 = 0.
Now, we solve for x by subtracting 0.5 from both sides: x = -0.5.
Therefore, the solution to the quadratic equation x^2 + x + 0.25 = 0 using the perfect square trinomial pattern is x = -0.5.
In order to determine at which step Jedida made a mistake, let's first go through the steps she followed to solve the quadratic equation:
Step 1: x^2 + 4x - 96 = 0
Jedida correctly added 4x to both sides, in order to move all x terms to one side of the equation.
Step 2: (x + 12)(x - 8) = 0
Jedida correctly factored the left side of the equation using the distributive property.
Step 3: x + 12 = 0 or x - 8 = 0
Jedida correctly used the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
Finally, Jedida solved for x by setting each factor equal to zero, and correctly found x = -12 and x = 8.
Therefore, Jedida did not make any mistakes in her solution. The correct answer is: She did not make any mistakes.