9.3 Solve Using Square Roots

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

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

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 +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

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 +15 +15 4𝑥 2 =0 4𝑥 2 4 = 0 4 𝑥 2 =0 𝑥 2 = 0 𝑥=0

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

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

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

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