Page 758 - Algebra 1

Example
1
___ = 2(1)
Solving a Quadratic Equation in Standard Form
Use the quadratic formula to solve x2 - 9x + 20 = 0 for x. SOLUTION
__ x = 2a
2
- b ± √ b - 4 a c
Use the quadratic formula. Substitute 1 for a, -9 for b,
and 20 for c.
Simplify.
-(-9) ± √(-9)2 - 4(1)(20)
= 9 ± √ 8 1 - 8 0 _ _
= 9± √1 = 9±1 _2_
22 x = 5 and 4
Check Verifythat5and4maketheoriginalequationtrue.
x2 -9x+20=0 (5)2 -9(5)+20 0 25 - 45 + 20 0
0=0 ✓
x2 -9x+20=0 (4)2 -9(4)+20 0 16 - 36+ 20 0
0=0 ✓
Rearranging Quadratic Equations before Solving
Use the quadratic formula to solve -18x + x2 = -32 for x.
SOLUTION Rearrange the equation into the standard form ax2 + bx + c = 0.
Example
2
Hint
Rearrange terms and their corresponding signs to match the form
ax2 +bx+c=0.
x2 -18x+32=0
Write the equation in standard form.
Use the quadratic formula. Substitute 1 for a, -18 for b,
and 32 for c.
Simplify.
-18x+x2 =-32 -18(2) + (2)2 -32 -36 + 4 -32
-32=-32 ✓ Lesson 110 743
__ x = 2a
2
- b ± √ b - 4 a c
___ = 2(1)
-(-18) ± √(-18)2 - 4(1)(32)
= 1 8 ± √ 3 2 4 - 1 2 8 __
= 1 8 ± √ 1 9 6 = 1 8 ± 1 4 _2_
22 x = 16 and 2
Check Verifythesolutionsforx. -18x+x2 =-32
-18(16) + (16)2 -32 -288 + 256 -32
-32=-32 ✓