Download Solving Equations Solve the following equations 1. 4x(x

Solving Equations
Solve the following equations
1. 4x(x-3) = 0
x = 0, x = 3
2. x2 – 5x + 6 = 0
x = 2, x = 3
3. x2 – 5x = 24
x = 8, x = -3
4. 3x3 – 27x = 0
x = 0, x = 3, x = -3
5. x2 + 22x + 121 = 0
x = -11
6. x2 + 9 = 0
No solution
7. Write a quadratic equation that has the solutions 3 and -5.
(x-3)(x+5) = x2 + 2x - 15
8. Write an equation that has the solutions 3, 4, and -2
(x-3)(x-4)(x+2) = (x2 – 7x + 12)(x+2) = (x3 -5x2 -2x + 24)
9. Write an equation that has the solutions ¾ and – ½ .
(4x-3)(2x+1) = 8x2 -2x -3
10. The area of a rectangle is 84 sq inches, and it has sides x+3 and x-2. Find the length and
the width of the rectangle.
(x+3)(x-2) = 84. x2 +x -6 – 84 = 0, x2 + x -90 = 0, (x+10)(x-9) = 0, x = -10, x = 9
reject -10 since can’t have a negative length. Sides are 12 and 7
11. The base of a triangle is twice its height. If the area of the triangle is 25 sq feet, what are
its base and height?
b = 2h, A = ½ bh = 25
h2 = 25, h = 5 feet, b = 10 feet
12. The length of a rectangle is 9 inches more than its width. If the area of the rectangle is
112 sq inches, find the length and width.
L = W+9. LW = (W+9)W = 112, W2 + 9W – 112 = 0 =(W+16)(W-7)
Can’t have W = -16, so W = 7 in, L = 16 in
13. The sum of a number and its square is 30, find the number.
n + n2 = 30; n2 + n – 30 = 0, n = - 6 or n = 5; both are appropriate solutions
14. The long leg of a right triangle is 10 miles more than the short leg, and the hypotenuse is
10 miles less than twice the shorter leg. Find the shorter leg.
S + 10 = L, H = 2S - 10
S2 + L2 = H2 by Pythagoras. S2 + (S+10)2 = (2S-10) 2
2s2 + 20s + 100 = 4s2 – 40s + 100, 2s2 - 60s = 0 s = 0 or s = 30; reject s = 0
short side is 30, long is 40, hypotenuse is 50