Solve the Quadratic Equation: 2(x - 5)^2 = 18

x=2 or x=8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2x2−20x+50=18

Step 2: Subtract 18 from both sides.

2x2−20x+50−18=18−18

2x2−20x+32=0

Step 3: Factor left side of equation.

2(x−2)(x−8)=0

Step 4: Set factors equal to 0.

x−2=0 or x−8=0

x=2 or x=8

1. x = 8

2. x = 2

Step-by-step explanation:

2 • (x - 5)2 -  18  = 0

2.1     Evaluate :  (x-5)2   =    x2-10x+25

3.1     Pull out like factors :

 2x2 - 20x + 32  =   2 • (x2 - 10x + 16)

3.2     Factoring  x2 - 10x + 16

The first term is,  x2  its coefficient is  1 .

The middle term is,  -10x  its coefficient is  -10 .

The last term, "the constant", is  +16

Step-1 : Multiply the coefficient of the first term by the constant   1 • 16 = 16

Step-2 : Find two factors of  16  whose sum equals the coefficient of the middle term, which is   -10 .

     -16    +    -1    =    -17

     -8    +    -2    =    -10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  -2

                    x2 - 8x - 2x - 16

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-8)

             Add up the last 2 terms, pulling out common factors :

                   2 • (x-8)

Step-5 : Add up the four terms of step 4 :

                   (x-2)  •  (x-8)

            Which is the desired factorization

2 • (x - 2) • (x - 8)  = 0

4.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

answer

you start with $5 and save $10 a week until you have at least $45wer

step-by-step explanation: