3. What are the solution(s) to the equation 5x2−14=591

Question

? Select all that apply(2 points)
Responses

−605−−−√
negative square root of 605

-11
-11

11
11

605−−−√
square root of 605
Question 2
4. What are the solution(s) to this equation? 98 = 2(x−2)2



(2 points)
x =


x=

Answer 1

To solve the equations given in your questions, we will go through them one by one.

Question 1: Solve the equation \( 5x^2 - 14 = 591 \)

1. Start by moving 591 to the left side of the equation: \[ 5x^2 - 14 - 591 = 0 \] \[ 5x^2 - 605 = 0 \]

2. Next, isolate \( x^2 \): \[ 5x^2 = 605 \] \[ x^2 = \frac{605}{5} = 121 \]

3. Now, take the square root of both sides: \[ x = \pm \sqrt{121} \] This gives us two solutions: \[ x = 11 \quad \text{and} \quad x = -11 \]

The correct answers are:

• \( -11 \)
• \( 11 \)

Question 2: Solve the equation \( 98 = 2(x - 2)^2 \)

1. Begin by dividing both sides by 2: \[ 49 = (x - 2)^2 \]

2. Now, take the square root of both sides: \[ \sqrt{49} = \pm (x - 2) \] This results in: \[ 7 = x - 2 \quad \text{or} \quad -7 = x - 2 \]

3. Solving each of these:

   • From \( 7 = x - 2 \): \[ x = 7 + 2 = 9 \]
   • From \( -7 = x - 2 \): \[ x = -7 + 2 = -5 \]

Thus, the solutions to this equation are:

• \( x = 9 \)
• \( x = -5 \)

Summary of Solutions

1. For the first equation \( 5x^2 - 14 = 591 \):

   • Solutions are \( -11 \) and \( 11 \).

2. For the second equation \( 98 = 2(x - 2)^2 \):

   • Solutions are \( x = 9 \) and \( x = -5 \).