Solving Square Roots Unit 3 Day 3

Warm Up Sometimes quadratic equations contain hidden information that is revealed when the equations are written in factored form. Change each quadratic equation below to an equivalent equation in factored form.

𝑦=−16 𝑡 2 −48𝑡 𝑦=5 𝑥 2 −10𝑥 𝑦=3 𝑥−1 +𝑥(𝑥−1)

𝑦=52 𝑥 2 −13 𝑦= 𝑥 2 +5𝑥+4 𝑦=𝑥 2𝑥+5 +𝑥(𝑥−10)

Interactive Notebook – Example 1 Isolate the radical Raise each side to the power of the index Solve for x Check for extraneous solutions

−8+ 5𝑥−5 =−3

9+5 3 2𝑥 =29

90−𝑥 =𝑥

Interactive Notebook – Example 2 Isolate one radical Raise each side to the power of the index Isolate the remaining radical (if needed) Solve for x Check for extraneous solutions

3 4𝑥−9 = 3 2𝑥−4

4 3𝑥+3 = 4 2𝑥−7

𝑥 +1= 𝑥+5

Interactive Notebook – Example 3 Isolate the radical Raise each side to the reciprocal power (If the numerator of the original exponent is even, the answer gets a ±) Solve for x Check for extraneous solutions

𝑥−27 3 2 =64

2𝑥+12 2 3 −3=13