1. 9.3 Solve Using Square Roots

2. What We Will Learn Solve quadratics by using square roots
Story problems

3. Essential question
How can you determine the number of solutions of a quadratic equation of the form 𝑎𝑥 2 +𝑐=0?

4. Ex. 1 Using Square Roots 3𝑥 2 −27=0 +27+27 3𝑥 2 =27 3𝑥 2 3 = 27 3
3𝑥 2 3 = 27 3
𝑥 2 =9
𝑥 2 = 9
𝑥=±3
Two solutions
𝑥 2 −10=−10
𝑥 2 =0
𝑥 2 = 0
𝑥=0
One solution
−5𝑥 2 +11=16
−11 −11
−5𝑥 2 =5
−5𝑥 2 −5 = 5 −5
𝑥 2 =−1
𝑥 2 = −1
No solution

5. Your Practice −3𝑥 2 =−75 𝑥 2 +12=0 −12 −12 4𝑥 2 −15=−15 +15 +15
−3𝑥 2 −3 = −75 −3
𝑥 2 =25
𝑥 2 = 25
𝑥=±5
𝑥 2 +12=0
−12 −12
𝑥 2 =−12
𝑥 2 = −12
No solution
4𝑥 2 −15=−15
4𝑥 2 =0
4𝑥 2 4 = 0 4
𝑥 2 =0
𝑥 2 = 0
𝑥=0

6. Ex. 2 solving 2 𝑥−1 2 =25 𝑥−1 2 = 25 𝑥−1=±5 𝑥−1=5, 𝑥−1=−5 +1 +1, +1 +1
𝑥−1 2 =25
𝑥−1 2 = 25
𝑥−1=±5
𝑥−1=5, 𝑥−1=−5
+1 +1,
𝑥=6, 𝑥=−4
Steps
1. Get by itself
both sides
3. solve for letter
4 𝑥−3 2 =36
4 𝑥− = 36 4
𝑥−3 2 =9
𝑥−3 2 = 9
𝑥−3=±3
𝑥−3=3, 𝑥−3=−3
𝑥=6, 𝑥=0

7. Your Practice 9 𝑥+1 2 +5=149 −5 −5 9 𝑥+1 2 =144 9 𝑥+1 2 9 = 144 9
9 𝑥 =149
− −5
9 𝑥+1 2 =144
9 𝑥 = 144 9
𝑥+1 2 =16
𝑥 = 16
𝑥+1=±4
𝑥+1=4, 𝑥+1=−4
−1 − −1 −1
𝑥=3, 𝑥=−5

8. Ex. 3 Approximating Square Roots
Solve and Round to nearest hundredth
4𝑥 2 −13=15
4𝑥 2 =28
4𝑥 2 4 = 28 4
𝑥 2 =7
𝑥 2 = 7
𝑥=±2.65

9. Ex. 4 Story Problem
A touch tank has a height of 3 feet. Its length is three times its width. The volume of the tank is 270 cubic feet. Find the length and width of the tank.
Need V = lwh
V = volume
l = length
w = width
h = height
V = 270
h = 3
l = 3w
w = w
270 = 3w(w)(3)
270= 9𝑤 2
270 9 = 9𝑤 2 9
30= 𝑤 2
30 = 𝑤 2
5.5=𝑤
l = 3(5.5)
l = 16.5