Page 714 - Algebra 1

Check x2 + 10x = 11 (-11)2 + 10(-11) 11
121 - 110 11 11=11 ✓
x2 +10x=11 (1)2 + 10(1) 11 1 + 10 11
11=11 ✓
Substitute -11 for x.
Simplify using the order of operations. Subtract.
Substitute 1 for x.
Simplify using the order of operations. Add.
Complete the square. Add the missing value to both sides of the equation.
Simplify the fraction.
Simplify.
Factor the left side. Simplify the right side.
Take the square root of both sides of the equation.
Simplify.
Write as two equations. Addition Property of Equality Simplify.
Substitute -1 for x.
Simplify using the order of operations. Add.
Substitute 9 for x.
Simplify using the order of operations. Add.
b. x2-8x=9 SOLUTION
x2 -8x=9
2 _8 2 _8 2
x -8x+(2)=9+(2)
x2 -8x+(4)2 =9+(4)2 x2 -8x+16=9+16 (x-4)2 =25
√ √(x-4)2=± 25
x - 4 = ±5 x-4=-5 or x-4=5
+__4 = +__4 x=-1 or
Check x2 -8x=9 (-1)2 - 8(-1) 9
1+8 9 9=9
x2 -8x=9 (9)2 - 8(9) 9 81 - 72 9 9=9
+__4 = +__4 x=9
✓
✓
In Example 2 the coefficient of each quadratic term is 1. The coefficient of the quadratic term must be 1 in order to use the completing-the-square method for solving quadratic equations. However, the coefficient of the quadratic term is often not 1. In which case, each term must be divided by the coefficient a.
Math Language
The quadratic term is the x2 term.
Lesson 104 699