M9: Using Square Roots to Solve Quadratic Equations

Question 1

What is a square root?

Answer 1

A number which produces a specified quantity when multiplied by itself.

Question 2

4 x^2 - 5 = 2

Answer 2

4 x^2 - 5 + 5 = 2 + 5 
4 x^2 = 7 
4x^2/4=7/4
x^2=1.75
x= +- √1.75
x≈+-1.32

Question 3

To simplify an expression, you can add ___?

Answer 3

like terms

Question 4

Completing the square is…?

Answer 4

a process of rewriting a quadratic expression as a perfect square trinomial so that it can
be solved by taking square roots

Question 5

5 - 2x^2 = -3

Answer 5

5-5-2x^2=-3-5
-2x^2/2=-8/2
x^2=-4
x=-2

Question 6

7x^2 + 10 = 18

Answer 6

7x^2+10-10=18-10
7x^2=8
x^2=8/7
x= √8/7

Question 7

How do you plug a standard form equation into the quadratic formula?

Answer 7

You determine your a, b, and c values and then plug it into the quadratic formula

Question 8

Are you confident with square roots? √96

Answer 8

The answer is close to 9.7

Question 9

What is a quadratic equation?

Answer 9

A quadratic equation is any equation having the form where x represents an unknown, and a, b, and c represent known numbers, with a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term

Question 10

16 x ^2 - 16x = 5

Answer 10

16x^2-16x=5
16x-4x=√5
12x=√5
x=√5/12

Question 11

x^2 + 6x = 2

Answer 11

x^2+6 = 2
X^2=-4
x=2

Question 12

Solve the equation by completing the square:

x^2 + 8x = 33

Answer 12

x^2 + 8x + 16 = 33 + 16
x^2 + 8x + 16 = 49
√(x+4)^2 = ±√49
x + 4 = ±7
x = 3 , 11

Question 13

Solve the equation by completing the square

x^2 - 6x = 8

Answer 13

x^2 – 6x + 9 = 8 + 9
x^2 – 6x +9 = 17
√(x - 3)^2 = ±√17	
x + 9 = ±√17
x = -9 ±√17