Question

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

Answer 1

Answer:

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.

Answer 2

Answer:

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