Question

Type the correct answer in each box. Use numerals instead of words.Consider the given quadratic equation.4x^2+8x+27=88In order to solve by completing the square, what number should be added to both sides of the equation?____ How many of the solutions to the equation are positive? _____What is the approximate value of the greatest solution to the equation, rounded to the nearest hundredth? _____

Answer 1

Given:

`4x^2+8x+27=88`

Find:

1) for to complete the square what number should be added to both side of the equation.

2) number of positive solution of the equation

3) value of greatest solution rounded to nearest hundredth.

Step-by-step explanation: 1)

`4x^2+8x+27=88`
`4x^2+8x=88-27`
`4x^2+8x=61`

in order to make it complete square we add

`4`

both side in the above equation , we get

`4x^2+8x+4=61+4`
`(2x+2)^2=(√(65))^2`

2) To find the solution to the equation

`4x^2+8x-61=0`

we have formula for finding roots of the equation.

`(-b\pm√(b^2-4ac))/(2a)=(-8\pm√(64-4(4)(-61)))/(2*4)`
`=(-8\pm√(64+976))/(8)`
`=(-8\pm√(1040))/(8)`
`√(1040)=32.25`

hence we have two cases

`(-8+32.25)/(8)=3.03125`

and

`(-8-32.25)/(8)=-5.03125`

hence only one solution to the equation is positive

3) we can clearly see from the above solution of the equation , the greatest solution to the equation is