Algebra 2 10 Questions Solve

Question

Solve the equation using any method.

x2 + 12x + 35 = 0

3x2 - 48 = 0

x2 + 10x + 25 = 64

-3x2 - 5x = 5

4x2 + 3x - 10 = 0

36x2 + 49 = 0

A golf ball is hit from the ground, and its height can be modeled by the equation h(t) = -16t2 + 128t, where h(t) represents the height (in feet) of the ball t seconds after contact. What will the maximum height of the ball be?

Write (1 - i) - (4 - 5i) as a complex number in standard form.

Write (-4 + 5i)(5 - i) as a complex number in standard form.

A company that produces video games has hired you to set the sale price for its newest game. Based on production costs and consumer demand, the company has concluded that the equation p(x) = -0.3x2 + 45x - 1000 represents the profit p (in dollars) for x individual games sold. What will the company’s profit be if it sells 100 games?

Answer 1

I'll answer two questions, but this will help you with the rest. I'm going to answer

x^2 + 12x + 35 = 0

36x^2 + 49 = 0

There are three methods you can use to solve quadratic equations: 1) Factoring 2) Completing the Square and 3) Quadratic Formula. Plus, one more method, Square Roots, that can be used sometimes. I will show you all of these. (To do well in Algebra, you need to learn all of the methods.)

The standard format of the a quadratic equation is ax^2 + bx + c = 0

Factoring: x^2 + 12x + 35 = 0

For this method, you ask yourself what two numbers add to b (12) and multiply to c (35). Well, 7 x 5 = 35. And 7 + 5 = 12. Yay! So this expression factors into (x+7)(x+5) = 0. There are only two values of x that make this equation true: x = -7 and x = -5. That's the answer.

Completing the square: x^2 + 12x + 35 = 0

For this method, you take half of b (12), which is 6, and square it to get 36. Then you need to add 1 and subtract 1 to the original expression so that 35 becomes 36: x^2 + 12x + 35 + 1 - 1 = x^2 + 12x + 36 - 1. Then you can factor this (using the method above) to get x^2 + 12x + 36 - 1 = (x+6)^2 - 1. So now we have (x+6)^2 - 1 = 0. Now you use the Square Roots method to find x. Add 1 to both sides to get (x+6)^2 = 1. Take the square root of both sides + or - (x+6) = 1. The two answers are x+6=1, which is x=-5 and -x-6 = 1, which is x=-7.

Quadratic formula: x^2 + 12x + 35 = 0

You should memorize this x = (-b + or - sqrt(b^2-4ac))/2a. Plugging the numbers in we get x = (-12 + or - sqrt(144-140))/2 = (-12 + or - 2)/2 = -6 + or - 1 = -5 or -7.

All three methods give the same answer.

The 2nd problem is harder. 36x^2 + 49 = 0

Factoring: b = 0 and c = 49. What two numbers add to zero and multiply to 49. You can look and look but there aren't any.

Completing the Square: It's already a square, so we can subtract 49 from both sides to get 36x^2 = -49 and divide both sides by 36 and get x^2 = -49/36. What number can you square and get a negative number. There aren't any!

Quadratic formula: (-0 + or - sqrt(0-7056))/72 But what's the square root of -7056. It's not possible to take the square root of a negative number.

It seems like there isn't any answer. But there is.

Math people defined a new symbol i, which is equal to the sqrt(-1). That is, i = sqrt(-1).

So let's use that to solve x^2 = -49/36 from above. Let's take the square root of both sides x = + or - sqrt(-49/36) We can split out the -1, so x = + or - sqrt(-1 x 49/36).

As a general rule, the sqrt(x) is the same thing as exponent x^1/2 and using the exponent rule (ab)^n = a^n x b^n, so we can say sqrt(ab) = sqrt(a)sqrt(b). So,

x = + or - sqrt(-1) x sqrt(49/36).

The sqrt(-1) is i. And the sqrt(49/36) = 7/6

So the answer is x = 7i/6 or x = -7i/6

This should help you with all the problems.