Question

➤ Activity 5: Complete Me!

Find the solutions of each of the following quadratic equations by completing the square. Answer
the questions that follow.
L x^2 -2x=3
2. s^2 +4s-21=0
3. t^2 +10t +9=0
4 x^2 + 14x = 32
5.x^2 -10r = -17

Answer 1

Explanation:

1. x^2 - 2x = 3

We first divide the -2 by 2 and square the answer

-2/2 = -1

(-1)^2 = 1

- now we add 1 to both sides:

x^2 - 2x + 1 = 3 + 1

x^2 - 2x + 1 = 4

(x - 1)^2 = 4

Take the square root of both sides:

x - 1 = +/- 2

x = +/- 2 + 1

x = -2 + 1 or 2 + 1

x = {-1, 3}.

The others are solved in a similar way:

2. s^2 + 4s - 21 = 0

s^2 + 4s = 21

4/2 = 2

2^2 = 4

Now we add 4 to both sides:

s^2 + 4x + 4 = 21 + 4

(s + 2)^2 = 25

s +2 = +/- sqrt25

s + 2 = +/-5

s = +/-5 - 2

s = {-7, 3}.

3. t^2 +10t +9=0

t^2 + 10t = -9

10/2 = 5

5^2 = 25

t^2 + 10t + 25 = -9 + 25

(t + 5)^2 = 16

t+5 = +/- 4

t = {-9, -1}.

4. x^2 + 14x = 32

x^2 + 14x + 49 = 32 + 49

(x + 7)^2 = 81

x + 7 = +/- 9

x = {-16, 2}.

5. x^2 - 10x = -17

x^2 - 10x + 25 = -17 + 25

(x - 5)^2 = 8

x - 5 = +/- sqrt8

x = -sqrt8 + 5 or sqrt8 + 5

= {2.17, 7.83} - correct to the nearest hundredth.