Question

Nikolas and Angela were trying to solve the equation: 3x² + 10x = 0. Nikolas said, 'I can complete the square. Half of 10 is 5, and 5 squared is 25. So I'll add 25 to both sides, factor, and solve.' Angela said, 'I'll factor the left-hand side of the equation as x(3x + 10) and solve using the zero product property.' Whose solution strategy would work?

1) Nikolas
2) Angela
3) Both
4) Neither

Answer 1

Both Nikolas and Angela's strategies would work to solve the equation 3x² + 10x = 0. Nikolas suggests completing the square and factoring, while Angela suggests factoring and using the zero product property. Both strategies lead to the same solutions.

Step-by-step explanation:

To solve the equation 3x² + 10x = 0, Nikolas and Angela each proposed different strategies. Nikolas suggested completing the square by adding 25 to both sides and then factoring. Angela suggested factoring the left-hand side of the equation as x(3x + 10) and using the zero product property to solve. Both strategies would work to find the solutions to the equation. Let's see how each strategy works:

1. Nikolas' Strategy:
   Step 1: Add 25 to both sides of the equation: 3x² + 10x + 25 = 25
   Step 2: Factor the left-hand side of the equation: (x + 5)(3x + 5) = 25
   Step 3: Solve for x by setting each factor equal to zero:
   x + 5 = 0 or 3x + 5 = 0
   x = -5 or x = -5/3
2. Angela's Strategy:
   Step 1: Factor the left-hand side of the equation: x(3x + 10) = 0
   Step 2: Set each factor equal to zero:
   x = 0 or 3x + 10 = 0
   x = 0 or 3x = -10 (subtract 10 from both sides)
   x = 0 or x = -10/3

Both Nikolas' and Angela's strategies result in the same solutions for the given equation, so the answer is 3) Both.