SOLUTION: What is the solution for this? Please use the 4 methods in quadratic equation to see the answer: *extracting the square root *Factoring *Completing the square and *Quadratic F

SOLUTION: What is the solution for this? Please use the 4 methods in quadratic equation to see the answer: extracting the square root Factoring Completing the square and Quadratic F

Question 886877: What is the solution for this?
Please use the 4 methods in quadratic equation to see the answer:
*extracting the square root
*Factoring
*Completing the square
and *Quadratic Formula
The sides of a square are increased to form a rectangle. One side is increased by 3 units and the other side is increased by 4 units. The area of the rectangle is 110 square units. What was the length of the side of the square?
Much thanks!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x be the side of the square, then
(x+4)*(x+3) = 110
x^2 +7x +12 = 110
x^2 +7x -98 = 0
1) can not use extracting the square root since polynomial is not a perfect square.
2) (x+14)*(x-7) = 0
x = -14 or 7
we need a positive value solution so we reject x = -14
the length of the side of the square is 7 units
3) x^2 +7x = 98
x^2 +7x + 49/4 = 98 + 49/4
(x + 7/2)^2 = 392/4 + 49/4 = 441/4
take square root of both sides of =
3.1) x + 7/2 = 21/2
x = 14/2 = 7
3.2) x +7/2 = -21/2
x = -28/2 = -14
4) x^2 +7x -98 = 0
x = (-b + or - square root(b^2 -4ac))/ (2a)
4.1) x = (-7 + square root(49 - 4*1*(-98))) / 2 = 7
4.2) x = (-7 - square root(49 - 4*1*(-98))) / 2 = -14

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