124 subtracted from the square of a number the result is five times the number find the negative solution

Answer 1

Hey, Rebecca Z.

The question should be 24 i guess,

Then, let the number be 'x'

x^2 - 24 { Since, 124 is subtracted from the square of a number }

x^2 - 24 = 5x {Since, The result is 5 times the number }

Bringing '5x' to the left of the equation, we get

x^2 - 5x - 24 =0

The above equation is in quadratic form.

Solving it by factorization.

-24 is taken and 24 factors are found out, we get 2*12, 3*8, 4*6, 1*24. But to get -5 when the two factors are added, we only have one, which is : 3*8

Hence, the factors are 3 and 8. To get -5 we have to take 3 - 8 =5 and 3 * (-8) = -24

x^2 + 3x - 8x -24 = 0

x(x + 3) -8 (x + 3) = 0

(x + 3) (x - 8) = 0

x = -3 , 8

So, x= -3 is the answer. As they asked for negative solution.

Hope this is helpful,

Sindhuja

Answer 2

x² - 124 = 5x

x² - 5x - 124 = 0

Use the quadratic formula to find x. Let a = 1, b = -5, and c = -124.

x = 5 ± [√(-5)² - 4(1)(-124)] / [2(1)] = 5 ± [√25 + 496] / 2 = 5 ± √521 / 2 = 13.91 or -8.91

The negative solution is x = -8.91.