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The numbers are: 49 and -4

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Q: What 2 numbers add up to 45 and multiply to -196?
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What 2 numbers add up to -45 and multiply to -196?

1) x + y = -45 2) xy = -196 solve for x in equation 2 by dividing both sides by y x= -196/y plug this value for x into the first equation -196/y + y = -45 subtract y from both sides -196/y = -45-y multiply both sides by -y 196 =45y + y2 subtract 196 from both sides 0 = y2 + 45y - 196 factor 0 = (y + 49)(y - 4) set each factor equal to 0 y + 49 = 0, y = -49 y - 4 = 0, y = 4 y = -49 or 4 plug these values back into equation 1 x + 4 = -45, x = -49 x + -49 = -45, x = 4 so the two numbers are 4 and -49 As two numbers are required that sum to -45 and multiply to -196, start off by working out the prime factorization of 196: 196 = 2 x 2 x 7 x 7. Using this, pairs of factors of 196 can be calculated: 1 x 196 2 x 98 4 x 49 7 x 28 14 x 14 As -196 is required, one factor must be positive and the other negative which means when they are summed, really their difference is calculated: 1 x 196 - difference = 195 2 x 98 - difference = 96 4 x 49 - difference = 45 7 x 28 - difference = 21 14 x 14 - difference = 0 A difference of 45 means the factors are 4 and 49, but as -45 is required, the larger factor must be negative, meaning the required numbers are 4 and -49 If you are in fact trying to factor a quadratic equation x2 - 45x - 196 = 0, you could also use the quadratic formula [-b + or - the square root of (b2-4ac)] / 2a so [-(-45) + or - the square root of ((-45)2 - 4(1)(-196)] / 2(1) [45 + or - square root of (2809)] / 2 [45 + or - 53] / 2 45 + 53 = 98, divide by 2 = 49 45 - 53 = -8, divide by 2 = -4 so the roots are (x - 49)(x + 4) so x = {49, -4}


What two numbers can you multiply to get 45?

9*5 = 45