If five is added to twice a certain number, the result is equal to twelve subtracted
from three times that number. Find the number.
Answers
Answer:
If five times a number is subtracted from twice the square of the number, the result is 63. What is the number?
x={-9/2,7}
PREMISES
2x^2-5x=63
ASSUMPTIONS
Let x=the number
CALCULATIONS
2x^2–5x=63
2x^2–5x-63=63–63
2x^2–5x-63=0 (Factor the polynomial and solve for the unknown “x” or if that is not possible, use the quadratic formula to solve)
2x^2–5x-63=0 can be factored:
(2x+9)(x-7)=0
Now, either 2x+9=0 and/or x-7=0
If 2x+9=0, then x=-9/2
If x-7=0, then x=7
So, tentatively, x=
{-9/2,7}
Test x={-9/2,7} in the original equation to see whether they are valid roots (zeros)
First, x=-9/2
2[(-9/2)^2]–5(-9/2)=63
2(81/4)-(-45/2)=63
162/4+45/2=63 (Convert the fractions to the common denominator 4)
162/4+90/4=63
(162+90)/4=63
252/4=63 and
63=63
x=-9/2 checks out as a valid root of the expression
Second, x=7
2(7^2)-5(7)=63
2(49)-35=63
98–35=63 and
63=63
x=7 checks out as a valid root of the expression
CONCLUSION(S)
x=
{-9/2,7}
C.H.