If 3 less than twice a number is equal to the negative square of the number and the number is positive, what is it’s value

Answer 1

Let x = the number

2x -3 = -sqrx

square both sides, but be careful to realize you've possibly injected an extraneous solution

x>0 so the false solution will probably involve a negative somewhere

4x^2 -12x + 9 = x

4x^2 -13x + 9 = 0

use the quadratic formula

x = 13/8 + or - (1/8)sqr(169-4(4)(9))

x = 13/8 + or - 5/8 = 18/8, 8/8 = 9/4, 1

check the answers to see if they both work

2(1)-3 =-sqr1

-1 = -1

2(9/4) - 3 = -sqr(9/4)

9/2 -6/2 = -3/2

3/2 does not equal -3/2

1 is the solution, but not 9/4

x =