SOLUTION: The sum of twice the square of a number and 7 times the number equals 15. What is the number? Twice the square of a number equals the sum of 5 times the number and 17. Find the

Question 972553: The sum of twice the square of a number and 7 times the number equals 15. What is the number?
Twice the square of a number equals the sum of 5 times the number and 17. Find the number
One number is 3 larger than another and the sum of their square is 269.Find the number.
Please help me!!!!
Found 3 solutions by stanbon, josgarithmetic, Boreal:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The sum of twice the square of a number and 7 times the number equals 15. What is the number?
2x^2 + 7x = 15
2x^2 + 7x - 15 = 0
2x^2 + 10x-3x - 15 = 0
2x(x+5)-3(x+5) = 0
(x+5)(2x-3) = 0
x = -5 or x = 3/2
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Twice the square of a number equals the sum of 5 times the number and 17. Find the number.
2x^2 = 5x+17
2x^2 - 5x - 17 = 0
x = [5 +- sqrt(25-4*2*-17)]/4
x = [5+-sqrt(161)]/4
x = [5+-12.69]/4
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One number is 3 larger than another and the sum of their square is 269.Find the number.
a = b + 3
a^2 + b^2 = 269
--------
(b+3)^2 + b^2 = 269
2b^2 + 6b = 260
b^2 + 3b -130 = 0
(b+13)(b-10) = 0
---
If b = -13, a = -10
If b = 10, a = 13
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Cheers,
Stan H.
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Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
The two problem descriptions are very literal. These are not tricky. Just transcribe exactly as described from the wording. The second problem might be seen as ambiguous, but there will only be two possible interpretations. TRY!
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
number is x
2x^2 +7x=15
2x^2-7x-15=0 I moved the 15 over to make it a quadratic equation =0
(2x-3) (x+5)=0 factoring, using 5 and 3.
;
x=(3/2), -5
;
Check -5: 50 -35=15
Check (3/2) : (9/2) +(21/2)=(30/2)=15
;
Number =x
2x^2=5x+17
;
do same thing
2x^2-5x-17=0
Try quadratic formula
;
(1/4) (5+/- sqrt (25+136)) This is the exact form of x: {-5 +/- sqrt (161)}/4
'
sqrt (161)=12.69
;
(1/4) 17.69=4.42
;
(1/4) (-7.69)=-1.92 ; x=-1.92,4.42 decimal
;
4.42^2 =19.53
twice that is 39.06
-5x=-22.1
-17 gets to 39.06 ;with rounding
(-1.92^2)*2=7.37
-5(-1.92)=9.6
9.6-17=-7.4 close enough with rounding
;

x is one number
x+3 the other
x^2 +x^2 +6x+9 ; (that is (x+3)(x+3) =269
;
2x^2+6x -260=0
x^2+3x-130=0 , dividing by 2.
(x+13)(x-10)=0
one number is 10, the other is 13
;
squared 10=100
square 13=169
sum is 269
;
One number is -13, the other is -10
They do the same thing. You need both solutions.
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