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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:
1) x2 - 5x - 14 = 0
2) x2 + 11x = -30
3) x2 - 45 = 4x
4) x2 = 15x - 56
5) 3x2 + 9x = 54
6) x3 = x2 + 12x
7) 25x2 = 5x3 + 30x
8) 108x = 12x2 + 216
9) 3x2 - 2x - 8 = 2x2
10) 10x2 - 5x + 11 = 9x2 + x + 83
11) 4x2 + 3x - 12 = 6x2 - 7x - 60
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Do on sheet:
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) Find 5 negative consecutive integers such the product of the 2nd and the 5th is 504.
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10) The area of a rectangle is 108 sq. feet. The length is 3 more than the width. Find the
perimeter. (must use let)
11) The area of a rectangle is 176 sq. feet. The width is 5 less than the length. Find the
perimeter. (must use let)
12) The area of a rectangle is 135 sq. feet. The length is 6 more than the width. Find the
perimeter. (must use let)
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13) Find 5 positive consecutive integers such the product of the 1st and the 5th is 221.
14) Find 4 consecutive negative odd integers such that the product of the 2nd and 4th is
357.
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Q3 Quiz 5 Review:
1) x2 – 14x = 15
2) x2 + 49 = -14x
3) 54 – 3x = x2
4) 8x2 + 192 = 88x
5) 2x3 + 30x2 + 112x = 0
6) 2x2 + 5x – 11 = 4x2 - 9x – 11
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7) 3x2 – 11x + 31 = 7x2 – 11x – 33
8) 10x3 = 20x2 + 240x
9) x2 + 4x = 96
10) 7x6 + 35x5 = 350x4
11) 8x2 – 3x + 17 = 7x2 – 8x + 17
12) 5x2 – 4x – 13 = 4x2 + 3x + 17
Answer Key:
1) x = {-1,15}
5) x = {-8,-7,0}
9) x = {-12,8}
3) x = {-9,6}
7) x = {-4,4}
11) x = {-5,0}
2) x = {-7}
6) x = {0,7}
10) x = {-10,0,5}
4) x = {3,8}
8) x = {-4,0,6}
12) x = {-3,10}
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Mixed Equations: Figure out what type of equation you have and then pick a
strategy to solve.
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
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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
20) x2 - 14 = 5x
18) 7(6x + 2) = 10(3x + 5)