fourteen times a number is 49 more than the square of the number. find the number
Answers
Step-by-step explanation:
let no. be x
ATQ
14 x= 49+x^2
x^2-14x+49=0
(x-7)^2=0
x=7
7 is the no.
Answer:
Step-by-step explanation:
LET THE NUMBER BE x
14 x = x² +49
- x² +14 x - 49 = 0
−x
2
+14x−49
Quadratic polynomial can be factored using the transformation ax
2
+bx+c=a(x−x
1
)(x−x
2
), where x
1
and x
2
are the solutions of the quadratic equation ax
2
+bx+c=0.
−x
2
+14x−49=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=
2(−1)
−14±
14
2
−4(−1)(−49)
Square 14.
x=
2(−1)
−14±
196−4(−1)(−49)
Multiply −4 times −1.
x=
2(−1)
−14±
196+4(−49)
Multiply 4 times −49.
x=
2(−1)
−14±
196−196
Add 196 to −196.
x=
2(−1)
−14±
0
Take the square root of 0.
x=
2(−1)
−14±0
Multiply 2 times −1.
x=
−2
−14±0
Factor the original expression using ax
2
+bx+c=a(x−x
1
)(x−x
2
). Substitute 7 for x
1
and 7 for x
2
.
−x
2
+14x−49=−(x−7)(x−7)