Quadratic Equation
1. x² - 3x - 28
(x+4)(x−7)
The middle number is -3 and the last number is -28.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -3
Multiply together to get -28
Can you think of the two numbers?
Try 4 and -7:
4+-7 = -3
4*-7 = -28
Fill in the blanks in
with 4 and -7 to get...
(x+4)(x-7)
Answer is (x+4)(x−7)
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2. x² - 8x = 9
9 or x=−1
Step 1: Subtract 9 from both sides.
x2−8x−9=9−9
x2−8x−9=0
For this equation: a=1, b=-8, c=-9
1x2+−8x+−9=0
Step 2: Use quadratic formula with a=1, b=-8, c=-9.
x =
x = 9 or x=−1
Answer is 9 or x=−1
3. 7, -2
5
7 - 2
7 + -2
= 5
Answer is 5
4. -4, 7
-28
7 × -4 = -28
Answer is -28
5. 5x² - x = 4x² + 2
2 or x=−1
Step 1: Subtract 4x^2+2 from both sides.
5x2−x−(4x2+2)=4x2+2−(4x2+2)
x2−x−2=0
For this equation: a=1, b=-1, c=-2
1x2+−1x+−2=0
Step 2: Use quadratic formula with a=1, b=-1, c=-2.
x = 2 or x=−1
Answer is 2 or x=−1
Step-by-step explanation:
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Answers & Comments
Quadratic Equation
1. x² - 3x - 28
(x+4)(x−7)
The middle number is -3 and the last number is -28.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -3
Multiply together to get -28
Can you think of the two numbers?
Try 4 and -7:
4+-7 = -3
4*-7 = -28
Fill in the blanks in
(x+_)(x+_)
with 4 and -7 to get...
(x+4)(x-7)
Answer is (x+4)(x−7)
••••••••••••••••••••••••••••••••••••••••••••••••••••••
2. x² - 8x = 9
9 or x=−1
Step 1: Subtract 9 from both sides.
x2−8x−9=9−9
x2−8x−9=0
For this equation: a=1, b=-8, c=-9
1x2+−8x+−9=0
Step 2: Use quadratic formula with a=1, b=-8, c=-9.
x =![\frac {-b ± √b² - 4ac}{2a} \frac {-b ± √b² - 4ac}{2a}](https://tex.z-dn.net/?f=%5Cfrac%20%7B-b%20%C2%B1%20%E2%88%9Ab%C2%B2%20-%204ac%7D%7B2a%7D)
x =![\frac {- (-8)² - 4(1)(-9)}{2(1)} \frac {- (-8)² - 4(1)(-9)}{2(1)}](https://tex.z-dn.net/?f=%5Cfrac%20%7B-%20%28-8%29%C2%B2%20-%204%281%29%28-9%29%7D%7B2%281%29%7D)
x =![\frac {8 ± √100}{2} \frac {8 ± √100}{2}](https://tex.z-dn.net/?f=%5Cfrac%20%7B8%20%C2%B1%20%E2%88%9A100%7D%7B2%7D)
x = 9 or x=−1
Answer is 9 or x=−1
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3. 7, -2
5
7 - 2
7 + -2
= 5
Answer is 5
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4. -4, 7
-28
7 × -4 = -28
Answer is -28
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5. 5x² - x = 4x² + 2
2 or x=−1
Step 1: Subtract 4x^2+2 from both sides.
5x2−x−(4x2+2)=4x2+2−(4x2+2)
x2−x−2=0
For this equation: a=1, b=-1, c=-2
1x2+−1x+−2=0
Step 2: Use quadratic formula with a=1, b=-1, c=-2.
x =![\frac {-b ± √b² - 4ac}{2a} \frac {-b ± √b² - 4ac}{2a}](https://tex.z-dn.net/?f=%5Cfrac%20%7B-b%20%C2%B1%20%E2%88%9Ab%C2%B2%20-%204ac%7D%7B2a%7D)
x =![\frac {- (-1) ± √(-1)² - 4(1)(-2)}{2(1)} \frac {- (-1) ± √(-1)² - 4(1)(-2)}{2(1)}](https://tex.z-dn.net/?f=%5Cfrac%20%7B-%20%28-1%29%20%C2%B1%20%E2%88%9A%28-1%29%C2%B2%20-%204%281%29%28-2%29%7D%7B2%281%29%7D)
x =![\frac {1 ± √9}{2} \frac {1 ± √9}{2}](https://tex.z-dn.net/?f=%5Cfrac%20%7B1%20%C2%B1%20%E2%88%9A9%7D%7B2%7D)
x = 2 or x=−1
Answer is 2 or x=−1
Step-by-step explanation: