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Solving Quadratic Equations
Solving quadratic equations (equations with x2 can be done in different ways. We will
focus on one method).
Solve by factoring:
After the equation is set equal to 0, you factor the trinomial.
x2 – 9x – 22 = 0
(x-11) (x+2) = 0
Now you would set each factor equal to zero and solve. Think about it, if the product of
the two binomials equals zero, well then one of the factors has to be zero.
x2 – 9x – 22 = 0
(x-11) (x+2) = 0
x – 11 = 0
+11
x = 11
x+2=0
+11
-2
or
-2
x = -2
* Check in the ORIGINAL equation!
Solving Quadratics by Factoring:
20) x2 - 5x - 14 = 0
21) x2 + 11x = -30
22) x2 - 45 = 4x
23) x2 = 15x - 56
24) 3x2 + 9x = 54
25) x3 = x2 + 12x
26) 25x2 = 5x3 + 30x
27) 108x = 12x2 + 216
29) 10x2 - 5x + 11 = 9x2 + x + 83
28) 3x2 - 2x - 8 = 2x2
30) 4x2 + 3x - 12 = 6x2 - 7x - 60
2
1) x2 + 44 = 15x
2) x2 + 81 = 18x
3) 315 – 10x = 5x2
4) x3 + 132x = 23x2
5) 7x2 + 12x + 16 = 4x2 - 9x + 16
6) 6x2 -9x + 13 = 7x2 - 9x - 51
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7) The area of a rectangle is 80 cm2. The width is stated as x + 3 and the length is
stated as x + 14. Find the value of x and then use x to find the perimeter.
8) The area of a rectangle is 117 in2. The width is 4 less than the length. Find the
perimeter of the rectangle.
9) The area of a rectangle is 108 sq. feet. The length is 3 more than the width. Find the
perimeter. (must use let)
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10) The area of a rectangle is 176 sq. feet. The width is 5 less than the length. Find the
perimeter. (must use let)
11) The area of a rectangle is 135 sq. feet. The length is 6 more than the width. Find the
perimeter. (must use let)
Mixed Equations: Figure out what type of equation you have and then pick a
strategy to solve. Do in NB.
1) 20 - (5/8)x = 40
2) 6(7x - 2) = 8(4x + 1)
3) 2(5x - 4) - 3(4x + 3) = -43
4) x2 + 44 = 15x
5) 3x2 + 18x = 81
6) 3x2 = 2x + 5
7) 11x - 5 = 7x - 53
8) 6(3x + 1) + 5(10 - 4x)= 39
9) ¼x - 33 = -49
10) 8x2 = 6x - 1
11) 9(3x + 1) = 8(5x + 6)
12) 15x = x2 - 16
13) x2 + x = 12
14) 9(4x + 7) - 6(7x + 10) = -54
15) 44 = 20 - 2x
16) 4x2 - 128 = 16x
17) 3x2 - 8x + 6 = x + 6
19) 3x2 + 13x - 12 = 9x2 - 11x - 12
18) 7(6x + 2) = 10(3x + 5)
20) 2x2 - 14 = 10x
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Consecutive Integer Problems
Write the “Let” for:
5 consecutive integers:
5 consecutive even integers 5 consecutive odd integers
1st =
1st =
1st =
2nd =
2nd =
2nd =
3rd =
3rd =
3rd =
4th =
4th =
4th =
5th =
5th =
5th =
1) Find 5 consecutive integers with the sum of 155.
2) Find 5 consecutive even integers such that the sum of the 3rd and 5th is 176.
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3) Find 4 consecutive odd integers such that the sum of the 1st and 4th is -108.
4) Find 5 consecutive integers such that the sum of the 3rd and the 4th is 35 less than 3
times the 1st.
5) Find 4 consecutive odd integers such that 5 times the 2nd is 58 more than the sum of
the 1st, 3rd, and 4th .
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7) Find 5 negative consecutive integers such the product of the 2nd and the 5th is 504.
8) Find 5 positive consecutive integers such the product of the 1st and the 5th is 221.
9) Find 4 consecutive negative odd integers such that the product of the 2nd and 4th is 357.