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Square Root Property
Name (Print):
Time/Day of Class:
The Square Root Property:
√
For a real number b, if a2 = b then a = ± b.
1. Use the model to apply the square root property:
(a) x2 = 18
√
x = ±√18√
x=± √
9 2
x = ±3 2
(b) 3x2 − 15 = 0
3x2 = 15
x2 = 5√
x=± 5
x2 = 75
5x2 − 55 = 0
(c) (x + 2)2 =√10
x + 2 = ±√10
x = −2 ± 10
(x − 3)2 = 27
(d) (3x − 7)2 =√−25
3x − 7 = ± −25
3x − 7 = ±5i
3x = 7 ± 5i
x = 7±5i
3
(2x − 5)2 = −9
Completing The Square:
Not every quadratic equation is formatted properly to have the Square Root Property applied to
it. To fix this we use Completing The Square. This works for any quadratic equation.
1. Divide both sides of the equation by the coefficient on x2 .
2. Get the constant term alone on one side of the equal sign.
3. Add the square of one half the coefficient on x to both sides.
4. Factor the variable side of the equation.
5. Apply the Square Root Property.
2. Completing The Square
(a) Why do we use Completing The Square?
(b) What do we add to both sides (step 3) to solve x2 + 4x = 1?
(c) What do we add to both sides (step 3) to solve x2 + 3x = 1?
(d) Solve x2 − 4x − 6 = 0.
(e) Solve 5x2 − 2x + 1 = 0.
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3. An auditor is checking some bank statements and sees that a bank account grew from 1000$
to 1210$ in two years. He cannot find a record of the interest rate for that account. Use
A = P (1 + r)t to find the interest rate (A = Final Amount, P = Principal (initial) investment,
r = interest rate as a decimal, t = time in years.
The exact value of r is
.
Use a calculator to estimate the approximate interest rate as
%.
4. What interest rate is needed to double an investment from 1000$ to 2000$ in two years? What
interest rate is needed to double an investment from 5000$ to 10, 000$ in two years? Use
A = P (1 + r)t .
5. Explain how the amount invested affects doubling time.
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