Devin wants to have equal amounts of room on all four sides of his ping pong table. A 5ft by 9ft table is placed in the center of a rectangular room that has an area of 221 square feet. What is the width of the clear space Devin will have on all sides of his table?
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since the width of the clear space needs to be equal but the length is unknown, make the width x. add the whole length and width of the room.
total length: x + 9 + x = 2x + 9
total width: x + 5 + x = 2x + 5
by multiplying the length and width, you would get the area of the room (221 sq ft). put in an equation.
(2x+9)(2x+5) = 221
F.O.I.L the equation.
4x^2 + 28x + 45 = 221
4x^2 + 28x - 176 = 0
x^2 + 7x - 44 = 0
obviously, there is no way this polynomial will factor out nicely so use the quadratic formula.
-b+|-√b^2 - 4ac / 2a
a = 1
b = 7
c = -44
plugin the numbers.
-7+|-√7^2 - 4(1)(-44) / 2(1)
solve for both positive and negative.
x = -7+|-√7^2 - 4(1)(-44) / 2(1)
x = -7+|-√49+176 / 2
x = -7+|-√225 / 2
x = -7 + 15 / 2 and -7 - 15 / 2
x = 4 or -11
since the width can't be a negative number, x = 4