Page 699 - Algebra 1

Solving Quadratic Equations Using Square Roots
LESSON 102
Warm Up
1. Vocabulary The of x is the number whose square is x. (13)
Simplify. 2. √ 81
(13)
4. √ 24 (46)
in the form x2 = a, can be solved by taking the square root of both sides. Solving x2 = a
Solve each equation.
a. x2=25
SOLUTION
Find the square root of both terms.
x2 = 25 2
Check x2 = 25 52 25
25=25 ✓
(46) 49
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3. -√ 25
_ 5. √ 9
(13)
Example
1
Math Reasoning
Verify Show by factoring that the equation x2 = 25 has the solution ±5.
√ x = ± √ 2 5 T a k e t h e s q u a r e r o o t o f b o t h s i d e s . x=5 or x=-5
You can combine the solutions using the ± symbol. x = ±5
x2 = 25 (-5)2 25
25=25 ✓
Math Reasoning
Analyze What is the relationship between squaring a number and taking the square root of a number?
b. x2 = -16
SOLUTION
Find the square root of both terms.
There is no real-number solution.
When the quadratic equation is in the form ax2 + c = 0, the square root can be taken after the variable is isolated.
x2 = -16 2
√ x = ± √ - 1 6 T a k e t h e s q u a r e r o o t o f b o t h s i d e s .
x ≠ ±√- 1 6 No real number squared can be negative.
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684 Saxon Algebra 1