Page 700 - Algebra 1

Example
2
Solving ax2 + c = 0 Solve each equation.
a. x2+3=52
SOLUTION
Isolate the variable and solve. x2 +3=52
Caution
When x2 equals a number other than 0, the equation has two solutions. Use the ± symbol after taking the square root.
-__3 -__3 x2 = 49
2
√ x = ± √ 4 9
x = ±7
Check x2 +3=52 72 +3 52
49+3=52 ✓
b. 4x2-100=0 SOLUTION
Isolate the variable and solve. 4x2 -100=0
+_ _ 1 0 _ 0 = +_ _ 1 0 _ 0
4x2 = 100
4x = 100 _2 _
44
Check
4x2 -100=0 4(5)2-100 0 4(25)-100 0 100-100 0
0=0 ✓
Addition Property of Equality Simplify.
Division Property of Equality
Simplify.
Take the square root of both sides. Simplify.
4x2 -100=0 4(-5)2 - 100 0 4(25) - 100 0 100 - 100 0
0=0 ✓
x2 = 25 2
√ x = ± √ 2 5 x = ±5
Subtraction Property of Equality Simplify.
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 . Simplify.
x2 +3=52 (-7)2 +3 52
49+3=52 ✓
Math Reasoning
Estimate How can √ 10 be estimated?
Numbers that are not perfect squares have irrational
roots. Irrational solutions can be expressed in square
root form: ±√x. An approximate answer can be
found using a calculator. To approximate √ 10 on a graphing calculator, press , and then
press .
Lesson 102 685