Is there a positive real number such that the sum of the number and its square is 1/4. If so, find the number.

Question

solve and type an equation

Answer 1

x+x^2=1/4

4x+4x^2=1

4x^2+4x-1=0

use the quadratic formula

(-4±√(16+16))/8

(-4±√32)/8

(-4±4√2)/8

(-1±√2)/2

(-1+√2)/2 is the number, or...

(-1+1.4142135624)/2

0.4142135624/2

0.2071067812 is the number

the radical form gives exactly 1/4 and the decimal form gives 0.2499999...