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WHAT TO DO: |
HOW TO DO IT: |
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1. Solve the equation x 2 + 4(x+1) 2 = (2x + 3) 2
Remove parentheses and simplify both sides:
Rewrite in standard equation form
and solve the equation: ⇒
Scratch: Find a numbers whose product is 5
with difference of 4 , larger sign "−".
Set each factor equal to zero:
The solution:
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x 2 + 4(x+1) 2 = (2x + 3) 2
x 2 + 4(x 2+2x+1) = 4x 2 + 12x +9
x 2 + 4x 2+8x+4 = 4x 2 + 12x +9
x 2 − 4x − 5 = 0
{5,1}
(x − 5)(x + 1) = 0
(x − 5) = 0 or (x + 1) = 0
x = 5 or x = − 1 |
| Check the original, equation
x 2 + 4(x+1) 2 = (2x + 3) 2 |
⇒ x = 5
⇒ x = -1 |
(5)2 + 4(5+1)2 = (2·5+3)2 , 25 + 144 =
139
(-1)2 + 4(-1+1)2 = (2·-1+3)2 , 1 + 0 =
1 |
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2. Solve the equation x 3 = 9x 2 − 20x
Rewrite in standard equation form
and solve the equation: ⇒
Factor out the common factor x ⇒
Scratch: Solve the inner equation: ⇒
Find a pair of numbers whose
product is 20 with sum of 9. sign "−".
Set each factor equal to zero:
The solution:
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x 3 = 9x 2 − 20x
x 3 − 9x 2 + 20x = 0
x (x 2 − 9x + 20) = 0
x (x 2 − 9x + 20) = 0
x (x − 5)(x − 4) = 0
x = 0, (x − 5) = 0 or (x − 4) = 0
x = 0, x = 4 or x = 3 |
| Check the original equation:
x 3 = 9x 2 − 20x |
⇒ x = 0:
⇒ x = 4:
⇒ x = 5 |
(0)3 = 9(0)2 − 20(0) , 0 = 0 - 0
(4)3 = 9(4)2 − 20(4) , 64 = 144 - 80
(5)3 = 9(5)2 − 20(5) , 125 = 225 - 100 |
