Taking Square Root of Both Sides

When solving a quadratic equation, when do you use the plus or minus (±) symbol?

• After taking the square root of both sides

• After adding the square to both sides

• After taking half of b

• After setting the equation equal to zero

Answer explanation

You use the ± symbol after taking the square root of both sides of a quadratic equation. This indicates that there are two possible solutions: one positive and one negative.

Choose the best method to solve this quadratic:

​ (a)  

3x² - 21 = 3

• Square Roots

• ZPP

• Quadratic Formula

Answer explanation

To solve the equation 3x² - 21 = 3, first simplify it to 3x² = 24. Dividing by 3 gives x² = 8. Taking the square root of both sides leads to the solution. Thus, the best method is Square Roots.

Solve:
x² - 49 = 0

• x = -7, x = 7

• x = -7

• x = 7

• x = -7, x = 1

Answer explanation

To solve x² - 49 = 0, factor it as (x - 7)(x + 7) = 0. Setting each factor to zero gives x - 7 = 0 (x = 7) and x + 7 = 0 (x = -7). Thus, the solutions are x = -7 and x = 7, making the correct choice x = -7, x = 7.

When do you use the plus or minus symbol?

• After taking the square root of both sides

• After adding the square to both sides

• After taking half of the x-term

• After setting the equation equal to zero

Solve by taking square roots:

5m² + 1 = 6

• m = 1

• m = 1 or -1

• m = √7

• m = 7/5 m = -7/5

Solve by square roots

k² - 6 = 43

• k = √37

• k = 37 or - 37

• k = 7, k = -7

• no solution

x² = 100

• 10

• 10 or -10

• 50

• 50 or -50

Solve by taking square roots:
a² + 9 = 9

• no solution

• a = 0

• a = 3 or -3

• a = 18

• Add 6 to both sides

• Square both sides

• Square root both sides

What is the first step to solve this equation?

• Add 6 to both sides

• Square both sides

• Square root both sides