Solve the equation 2x2+8x -1 = 0
by completing the square.
Give your answers correct to 2 decimal places.

x ≈ - 4.12 , x ≈ 0.12

Step-by-step explanation:

2x² + 8x - 1 = 0 ( add 1 to both sides )

2x² + 8x = 1 ( factor out 2 from the first two terms )

2(x² + 4x) = 1

To complete the square

add/ subtract ( half the coefficient of the x- term )² to x² + 4x

2(x² + 2(2)x + 4 - 4) = 1

2(x + 2)² - 8 = 1 ( add 8 to both sides )

2(x + 2)² = 9 ( divide both sides by 2 )

(x + 2)² = ( take square root of both sides )

x + 2 = ± = ± ( subtract 2 from both sides )

x = - 2 ±

Then

x = - 2 - ≈ - 4.12 ( to 2 dec. places )

x = - 2 + ≈ 0.12 ( to 2 dec. places )

The answer is in the image 

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

The answer is in the image 

The answer is in the image 

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The answer is in the image 

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

There are 6 outcomes 1,2,3,4,5,6

Total outcomes = 6

Outcomes when rolling a number is 4 or less = 1,2,3,4

Total outcome when rolling a number is 4 or less=4

Probability = required outcome/total outcome

                 =4/6

                 =2/3

Therefore probability = 2/3