Solve by completing the square. .

the solutions are 0 and 7

Step-by-step explanation:

4r²-28r=-49 take out the 4 to make it a simple trinomial

4(r²-7r)=-49 find half of 7 and square it

4(r²-7r+12.25)=-49 now factor

4(r-3.5)²=-49 divide by 4

(r-3.5)=-12.25 now square root bother sides

r-3.5=+/-3.5 add 3.5

r=3.5+3.5 =7

r=-3.5+3.5=0

idk

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4