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

Question

? Select all that apply(2 points)
Responses

11
11

-11
-11

−605−−−√
negative square root of 605

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=

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Answer 1

Let's solve each equation step by step.

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

1. Isolate the quadratic term: \[ 5x^2 = 591 + 14 \] \[ 5x^2 = 605 \]

2. Divide both sides by 5: \[ x^2 = \frac{605}{5} = 121 \]

3. Take the square root of both sides: \[ x = \pm \sqrt{121} \] \[ x = \pm 11 \]

So, the solutions for this equation are:

• 11
• -11

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

1. Isolate the squared term: \[ 98 = 2(x - 2)^2 \] Divide both sides by 2: \[ 49 = (x - 2)^2 \]

2. Take the square root of both sides: \[ x - 2 = \pm \sqrt{49} \] \[ x - 2 = \pm 7 \]

3. Solve for \( x \):

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

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

Thus, the solutions for this equation are:

• \( x = 9 \)
• \( x = -5 \)

Summary of Responses:

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

   • Correct responses: 11 and -11

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

   • Solutions: \( x = 9 \) and \( x = -5 \)