complete the exercises in the “Projects” section on page 331 of Mathematics in Our World.
You should be concise in your reasoning. For Project #1, work only equations (a) and (c), but complete all 6 steps (a-f) as shown in the example.
For Project #2, please select at least five numbers; 0 (zero), two even, and two odd. Make sure you organize your paper into separate projects.
1. An interesting method for solving quadratic equations
came from India. The steps are
(a) Move the constant term to the right side of the
(b) Multiply each term in the equation by four times
the coefﬁcient of the x
(c) Square the coefﬁcient of the original x term and
add it to both sides of the equation.
(d) Take the square root of both sides.
(e) Set the left side of the equation equal to the
positive square root of the number on the right side
and solve for x.
(f) Set the left side of the equation equal to the
negative square root of the number on the right side
of the equation and solve for x.
Example: Solve x
+ 3x − 10 = 0.
+ 3x = 10
+ 12x = 40
+ 12x + 9 = 40 + 9
+ 12x + 9 = 49
2x + 3 = ±7
2x + 3 = 7
2x = 4
x = 2
2x + 3 = −7
2x = −10
x = −5
− 2x − 13 = 0
− 4x + 3 = 0
+ 12x − 64 = 0
− 3x − 5 = 0