Yes, x=−3 is a solution because substituting it back into the equation results in the following:

Question

x Substituted Evaluate True Statement?
−3 −3(−3)2−9(−3)=0 0=0 True

true or false

Answer 1

The statement is true.

To verify:

1. Substitute \( x = -3 \) into the equation \( -3x^2 - 9x = 0 \).
2. Calculate: \[ -3(-3)^2 - 9(-3) \ = -3(9) + 27 \ = -27 + 27 \ = 0 \]

The left side evaluates to \( 0 \), which equals the right side (also \( 0 \)). Therefore, the statement confirms that \( x = -3 \) is indeed a solution to the equation.

Answer 2

Show how many solutions are in the solution set for the equation 3x^2=21 .(1 point)

Answer 3

To determine the number of solutions for the equation \( 3x^2 = 21 \), we can follow these steps:

1. Simplify the equation: \[ 3x^2 = 21 \] Divide both sides by \( 3 \): \[ x^2 = 7 \]

2. Solve for \( x \) by taking the square root of both sides: \[ x = \pm\sqrt{7} \]

This results in two solutions: \[ x = \sqrt{7} \quad \text{and} \quad x = -\sqrt{7} \]

Therefore, the solution set contains 2 solutions.

Answer 4

Show how many solutions are in the solution set for 2(x−5)^2+2=20 .(1 point)
Responses

Answer 5

To determine the number of solutions for the equation \( 2(x-5)^2 + 2 = 20 \), we'll follow these steps:

1. Subtract 2 from both sides: \[ 2(x-5)^2 + 2 - 2 = 20 - 2 \] This simplifies to: \[ 2(x-5)^2 = 18 \]

2. Divide both sides by 2: \[ (x-5)^2 = 9 \]

3. Take the square root of both sides: \[ x-5 = \pm 3 \]

4. Solve for \( x \):

   • For \( x - 5 = 3 \): \[ x = 3 + 5 = 8 \]
   • For \( x - 5 = -3 \): \[ x = -3 + 5 = 2 \]

So the solutions are \( x = 8 \) and \( x = 2 \).

Therefore, the solution set contains 2 solutions.