What should be the first step when solving the quadratic equation below?

Question

(x+10)^2−25=36


(1 point)
Responses

Divide both sides of the equation by 2.

Subtract 10 from both sides of the equation.

Add 25 to both sides of the equation.

Take the square root of both sides of the equation.

Answer 1

The first step when solving the quadratic equation \((x+10)^2−25=36\) is to:

Add 25 to both sides of the equation.

This will simplify the equation to an easier form for further solving. So the correct response is:

Add 25 to both sides of the equation.

Answer 2

Answer the questions about this quadratic equation shown below.

(x−3)^2/5=20

(3 points)
What should be the first step when solving the quadratic equation above?

Which of the following is one of the solutions to the quadratic equation above?

Which of the following is the other solution to the quadratic equation above?

Answer 3

Let's solve the equation step by step. The given equation is:

\[ \frac{(x-3)^2}{5} = 20 \]

1. What should be the first step when solving the quadratic equation above?

The first step is to eliminate the fraction by multiplying both sides by 5:

\[ (x-3)^2 = 100 \]

2. Which of the following is one of the solutions to the quadratic equation above?

Next, we take the square root of both sides to solve for \(x\):

\[ x-3 = \pm 10 \]

This gives us two cases to consider:

1. \(x - 3 = 10\)

   • \(x = 13\)

2. \(x - 3 = -10\)

   • \(x = -7\)

3. Which of the following is the other solution to the quadratic equation above?

From our solutions:

• One solution is \(x = 13\)
• The other solution is \(x = -7\)

So, depending on the options given, you will identify \(13\) as one solution and \(-7\) as the other solution.

Answer 4

Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (5x+1)(x−8)=0
?(1 point)
Responses

At least one of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.

No values of x will make the left side of the equation equal 0.

Neither of the factors, (5x+1)or (x−8), must equal 0 for the left side of the equation to equal 0.

Answer 5

Based on the Zero Product Property, the correct statement regarding the quadratic equation \((5x+1)(x−8)=0\) is:

At least one of the factors, (5x+1) or (x−8), must equal 0 for the left side of the equation to equal 0.

This is the essential principle behind the Zero Product Property: if the product of two factors equals zero, at least one of the factors must be zero.

Answer 6

While using the Zero Product Property to find the solutions for the quadratic equation (x−2)(x−9)=0
, a student completed the work below. Is the student's work correct?

(x−2)(x−9)=0
original equation



Solution #1:

x−2=0


x=2




Solution #2:

x+9=0


x=−9




(1 point)
Responses

No, there should be a solution #3.

No, x−9=0 should have been used to find solution #2.

Yes, the student answered the problem correctly.

No, x+2=0 should have been used to find solution #1.

Answer 7

Let's review the student's work on the equation \((x−2)(x−9)=0\).

1. Original equation: \((x−2)(x−9)=0\) (correct)

2. Solution #1:

   • The student correctly solved \(x−2=0\):
   • \(x=2\) (correct)

3. Solution #2:

   • Here, the student incorrectly wrote \(x+9=0\). The correct factor should be \(x−9=0\):
   • This leads to \(x=9\) (not \(-9\), as the student stated).

Given this analysis, the most accurate response is:

No, x−9=0 should have been used to find solution #2.

Answer 8

Solve the quadratic equation 5x(x+12)=0
using the Zero Product Property.(1 point)
Responses

.
The solution set is x={1/12, 1/5}
.

.
The solution set is x={0, 12}
.

.
The solution set is x={−12, 0}
.

The solution set is x={5, 12}
.

Answer 9

To solve the quadratic equation \(5x(x+12) = 0\) using the Zero Product Property, we set each factor equal to zero:

1. \(5x = 0\)
2. \(x + 12 = 0\)

Now, solving each of these:

1. From \(5x = 0\):

   • Divide both sides by 5:
   • \(x = 0\)

2. From \(x + 12 = 0\):

   • Subtract 12 from both sides:
   • \(x = -12\)

Thus, the solution set is:

\[ x = {-12, 0} \]

So the correct response is:

The solution set is x={−12, 0}.