Question

Part D. Natasha is solving the following quadratic equation and believes she has made a mistake.

Step 1: 2x^2 + 5x = 3
Step 2: 2(2x – 5) = 3
Step 3: x = 3 and 2x – 5 = 3
Step 4: x = 3 and x = 4
Identify where Natasha made her mistake and explain her misconception. Solve the equation showing all work?
A) Step 2
B) Step 3
C) Step 4
D) There is no mistake.

Answer 1

Natasha made her mistake in Step 3 where she solved for x incorrectly as 4 instead of 6.5.

Step-by-step explanation:

Natasha made her mistake in Step 3. Instead of solving for x in the equation 2x - 5 = 3, she incorrectly solved for x as 4. However, the correct solution is x = 4 + 5/2 = 6.5.

To solve the quadratic equation 2x^2 + 5x - 3 = 0, we can either factor it or use the quadratic formula. Factoring, we get (2x - 1)(x + 3) = 0. Setting each factor equal to zero, we find x = 1/2 and x = -3.

So the correct solution to the equation is x = 6.5, 1/2, -3.