geno3141

h² + 14h + 3  =  5

The form that you must have:

-- the squared term must have a coefficient of 1

-- the left side must have the squared term and the linear term; the number must be on the right side.

First, move the 3 to the other side (by subtracting 3 from both sides):

h² + 14h        = 2

There are three steps in completeing the square:

--  divide the coefficient of the linear term by 2       14 ÷ 2  =  7

-- square that result                                                    7²  =  49

-- add this number to both sides.

h² + 14h + 49  =  2 + 49

(h + 7)(h + 7)  =  51                                        Factor:

       (h + 7)²  =  51                                          Find the square root:

         h + 7  =  ±√51                                        Removd the 7 from the left side:

               h  =  -7 ±√51

6 / (6b + 4)  =  2 / (b - 4)

Cross multiply:  6(b - 4)  =  2(6b + 4)

Distribute:        6b - 24  =  12b + 8

Subtract 6b:         - 24  =  6b + 8

Subtract 8:           - 32  =  6b

Divide by 6:          -16/3  =  b

(60x - 48000) · .7  =  .7 · (60x - 48000)

Use the Distributive Law:     =  (.7)·(60x) - (.7)·(48000)

                                          =  42x - 33600

[36x^(1/4)]^1.5

=  [36]^1.5 · [x^(1/4)]^1.5

If you have an exponent to an exponent, multiply the exponents together:  (1/4) x 1.5  =  3/8

=  [36]^1.5 · [x]^(3/8)

An exponent of 1.5 is an exponent of 3/2 which means cube it and find the square root (either order);:

=  216 · x^(3/8)

Problems are frequaently easier to solve if they have no denominators; multiply both sides by 4:

    4 x 1/4 (4x + 10)  =  4 x 8

         4x + 10  =  32

Subtract 10:

         4x  =  22

Divide by 4:

        4x  =  5.5

2a + 9  =  6a - 15

Get all the variable on one side; since 6a is bigger than 2a, subtract 2a from both sides:

2a - 2a + 9  =  6a - 2a - 15

     9  =  4a - 15

Add 15 to both sides:

     9 + 15  =  4a - 15 + 15

     24  =  4a

Divide both sides by 4:

     24 / 4  =  4a / 4

      6  =  a

It is just usual to use x.

Letters such as a, b, c, d, and e are often reserved for constants and u, v, w, x, y, and z are usually reserved for variables.

There is no mathematical "rule"  that requires that you use x for the variable.

3/14 x 8/18 x 12/20

Reduce 8/18 to 4/9 by dividing both by 2  --->  3/14 x 4/9 x 12/20

Reduce 12/20 to 3/5 by dividing both by 4  --->  3/14 x 4/9 x 3/5

The two 3's will cancel out the 9  --->  1/14 x 4/1 x 1/5

Reduce the 4 and the 14 by dividing both by 2   --->  1/7 x 2/1 x 1/5

Multiply the numerators together and the denominators together  --->  2/35

9C2  =  9! / ( 2! · (9-2)! )  =  9! / ( 2! · 7! )  =  36

I'm assuming that you want an exact answer, not a graphical approximation (which is a lost easier!):

x² + y²  =  325  ===>  x² + 2xy + y²  =  325 + 2xy  ===>  (x + y)²  =  325 + 2·6(x + y)

===>  (x + y)²  =  325 + 12(x + y)     ===>  (x + y)² - 12(x + y) - 325  =  0

Factor or use the quadratic formula:  [(x + y) - 25][(x + y ) + 13]  =  0

===>  x  =  25    or    x  =  -13

If x + y  =  25    ===>     y  =  25 - x

x² + y²  =  325   ===>   x² + (25 - x)²  =  325   ===>   x² + 625 - 50x + x²  =  325

===>   2x² - 50x + 300  =  0   ===>   x² - 25x + 150  =  0 

Factoring:  (x - 15)(x - 10)  =  0   ===>  x  =  15     or     x  =  10

===>  when x  =  10,  y  =  15; when x = 15, y = 10

Now, x = -13  gives you two more answers; in a similar solution as the above:  x  =  (-13 ± √481 ) / 2

When x = (-13 + √481 ) / 2, y = (-13 - √481 ) / 2  

and  when x = (-13 - √481 ) / 2, y = (-13 + √481 ) / 2