Solving for Quadratic by Taking the Square Root of Both Sides

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.

Tags

CCSS.8.EE.A.2

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Choose the best method to solve this quadratic:

​ (a)  

-3 = 4x² + 9x

• Quadratic Formula

• Square Roots

• ZPP

Answer explanation

The equation can be rearranged to standard form: 4x² + 9x + 3 = 0. Since it is a quadratic equation, the Quadratic Formula is the best method to find the roots, as it applies to any quadratic in the form ax² + bx + c.

Tags

CCSS.HSA-REI.B.4B

What is another word for zeros?

• y-intercepts

• roots

• vertex

• axis of symmetry

Answer explanation

In mathematics, 'zeros' refer to the values of a function where it equals zero. These are also known as 'roots'. The other options like y-intercepts, vertex, and axis of symmetry refer to different concepts in graphing.

Tags

CCSS.HSF-IF.C.7C

9k² = 225

• 4

• 4, -4

• 25, -25

• -5, 5

Answer explanation

To solve 9k² = 225, divide both sides by 9 to get k² = 25. Taking the square root gives k = ±5. Thus, the correct answers are -5 and 5.

Tags

CCSS.8.EE.A.2

Solve.
n² - 5 = -4

• n = ±√9

• n = ±3

• n = ±1

• No real solution

Answer explanation

To solve n² - 5 = -4, add 5 to both sides: n² = 1. Taking the square root gives n = ±1. Thus, the correct answer is n = ±1.

Tags

CCSS.8.EE.A.2