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Zinaida [17]
3 years ago
15

Which are steps in the process of completing the square used to solve the equation 3 – 4x = 5x2 – 14x? Check all that apply

Mathematics
1 answer:
blsea [12.9K]3 years ago
3 0

Answer:

B)3 = 5x2 – 10x

D)8 = 5(x2 – 2x + 1)

G)  = (x – 1)2

Step-by-step explanation:

Given quadratic : 3 - 4x = 5x2 - 14x

We need to apply completing the square to solve the equation.

First step is to get rid 4x from left side.

We can add 4x on right side to get rid from left side.

3 = 5x^2-14x+4x

On simplifying this step, we get

3 = 5x^2-10x

Now, we need to factor out 5 from right side to get the coefficient of x^2 as 1.

We get,

3 = 5(x^2-2x)

Now, coefficient of x is -2. So, we need to add half of the square of -2.

-2/2 = -1.

And square of -1 is 1.

Therefore, adding 1 inside parenthesis and 5×1 = 5 on left side, we get

3+5 = 5(x^2 -2x+1)

8 = 5(x^2 -2x+1)

Let us find the perfect square of (x^2 -2x+1).

(x^2 -2x+1) = (x-1)^2

Therefore, we get

8 = 5(x-1)^2.

So, the above highlighted are steps in the process of completing the square.

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A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all arou
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Complete question :

A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all around the patio.The perimeter of the patio after it is expanded is 74 feet. The equation which represents x, the width of the border is 2[(12+2x)+15+2x)]=74. What is the width of the border?

1) 2 1/2 feet

2) 3 feet

4) 5 feet

5) 8 1/2 feet

Answer:

2.5

Step-by-step explanation:

Solving for X in the perimeter equation :

2[(12+2x)+15+2x)]=74

Open the bracket

2[(12 + 2x + 15 + 2x)] = 74

2(27 + 4x) = 74

54 + 8x = 74

8x = 74 - 54

8x = 20

x = 20/8

x = 2.5

Hence, width fo border = 2.5

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