Solve the equation by using the quadratic formula round to the nearest tenth if needed 10x^2-5x-25=0 A) the solutions are about -5.2 and 2.5 B) the solutions are about -1.8 and 2.3 C) the solutions are -2 and 1 D) the solutions are about -1.4 and 1.9 E) the solutions are -5 and 10

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Answered on Fri May 20 2022

Quadratic formula :

x =[ -b ± √ b² - 4ac]/2

We have,

10x^2-5x-25=0

here, a = 10, b = -5 , c = -25

x = [-(-5) ± √(-5)² - 4(10)(-25)]/2×10

x = [ 5 ± √25 + 1000]/20

x = [ 5 ± √1025]/20

x = [ 5 ± 32.01]/20

Now, taking positive sign,

x = [5 + 32.01]/20

x = 37.01/20

x = 1.8507 or 1.9

Now, taking negative sign

x = [5 - 32.01]/20

x = - 27.01/20

x = -1.3505 or - 1.4

Hence, option (D) is correct .