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

User BlueBird
by
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2 Answers

4 votes

Answer:

1. x = 8

2. x = 2

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.

User Scott Jacobsen
by
7.8k points
2 votes

Answer:

x=2 or x=8

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

User Bushes
by
8.1k points

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