Question

Type the correct answer in each box. Use numerals instead of words.

Consider the given quadratic equation.



In 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

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1.) The number to be added on both sides is = 1

2. ) only 1 solution is positive, other one is negative

3.)The aprrox value may be 2

Answer 2

(a) 1

(b) 1

(c) 3.03

Explanation:

The given quadratic equation is

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

Subtract 27 from both sides.

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

`4x^2+8x=61`

Taking out common factor.

`4(x^2+2x)=61`

Divide both sides by 4.

`x^2+2x=(61)/(4)`

If an expression is
`x^2+bx`, then we need to add
`((b)/(2))^2`, to make it perfect square.

Here, b=2, so
`((2)/(2))^2=1`

Add 1 on both sides.

`x^2+2x+1=(61)/(4)+1`

`(x+1)^2=(65)/(4)`

Taking square root on both sides.

`(x+1)=\pm \sqrt{(65)/(4)}`

Subtract 1 from both sides.

`x=-1\pm \sqrt{(65)/(4)}`

`x=-1\pm 4.03`

`x=-1+4.031` and
`x=-1-4.031`

`x=3.031` and
`x=-5.031`

Only one solution is positive.

Greatest solution is 3.031, therefore the approximate value of this solution is 3.03.