Need help understanding algebra

1.Solve the equation
X^2- 48x- 49=0
The answer is -1,49 but how do I get the answer
2.A projectile is fired upward from the ground with an initial velocity of 500ft per second. Neglecting air resistance, the height of the projectile at any time t can be described by the polynomial -16t^2 +500t. Find the height of the projectile at t=6seconds.
The answer is 2424ft. but how do I get it.
3.If the sides of a square are increased by 2 meters, the area becomes 81 square meters. Find the length of a side of the original square.
The answer is 7 meters, but how do I get it?

To factor x² - 48x - 49, you need two numbers whose product is -49 and sum is -48:
1 * -49 = -49
1 + -49 = -48

x² - 48x - 49 = 0
(x + 1) (x - 49) = 0
x + 1 = 0 or x - 49 = 0
x = -1, 49

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2.

Just plug t = 6 into equation:

h(t) = -16t² + 500t
h(6) = -16(36) + 500(6) = -576 + 3000 = 2424

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3.

Length of sides of original square = x, where x > 0

Sides of square are increased by 2 meters: x + 2
Area is now = 81

(x + 2)² = 81
x + 2 = 9 (we ignore x + 2 = -9, since x > 0, and x + 2 > 2)
x = 9 - 2
x = 7

Note:

These are all very simple problems. If you are having so much trouble solving, you should ask your teacher or parents for extra help, or perhaps get a tutor. Good luck.

Mαthmφm

1. Got to admit, this one has me stumped


2. Given the equation to start, this is simple substitution:

Where t = 6

-16 * 6^2 + 500 * 6 =

3. Let the initial length of the squares sides in meters equal x. The size of the new squares sides are therefore x + 2. Now we know the following:

(x + 2)^2 = 81 The length of the new squares sides squared equals 81 square meters. Let's take the square root of each side.

x + 2 = 9