Question

Typethe correct answer in each box. 4x^2+8x+27=88 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

The first box is 1, the second box is 1, and the third box is 3.03

Explanation:

Answer 2

1.what number should be added to both sides of the equation? 1

2. how many of the solutions to the equation are positive? one, x=3.031

3.what is the approximate value of the greatest solution to the equation rounded to the nearest hundredth? 3.03

Explanation:

The question is on solving for quadratic equations using the completing square method

The equation given is ;

4x²+8x+27=88...........rewrite the equation

4x²+8x+27-88=0

4x²+8x+-61=0...................divide every term of the equation by 4

4x/4²+8x/4+-61/4=0/4

x²+2x-15.25=0..................rewrite the equation as;

x²+2x=15.25.......................complete square on both sides

x²+2x+ (2/2)²= 15.25 +(2/2)²

x²+2x+1 = 15.25+1

x²+2x+1=16.25................factorize the left hand side

(x+1)²=16.25.....................eliminate the root on the left hand side

x+1=±√16.25

x+1= ± 4.031

solutions

x+1= +4.031

x= +4.031-1 =3.031

or

x+1= -4.031

x= -4.031-1 = - 5.031