solve for x 16 xx025x025xSolutionWe have 16xx 025 x 025 x

solve for x:

1.6= (x)(x)/(.025-x)(.025-x)

Solution

We have 1.6=(x)(x)/( 0.25 – x)( 0.25 –x) = x²/( 0.25 –x)² or, 1.6( 0.25 – x)² = x² or, 1.6( 0.0625 – 0.5x + x²) = x² or, 1.6x² –x² -0.8x + 0.1 = 0 or, 0.6x² -0.8x + 0.1 = 0. On multiplying both the sides by 10, we have 6x² -8x + 1 = 0. Now, on using the quadratic formula, we have x = [-(-8) ± {( -8)² -4*6* 1} ]/2*6 = [ 8 ± ( 64 – 24)]/12 =( 8 ± 40)/12 = (2/3) ± (10)/6.

Notes: