It is quadratic equation. First we have find delta given by formula: delta= b 2 − 4 a c where our a=16 b=-24 c=7 so, delta= 2 4 2 − 4 ∗ 16 ∗ 7 = 128 Because delta is positive, there is real results. Now we can use next formula x= 2 a − b + d e lt a , to find roots (results, 2 results because its quadratic equation and delta is greater than 0) x1= 2 ∗ 16 24 + 128 = 4 3 + 2 x2= 2 ∗ 16 24 − 128 = 4 3 − 2
16 x 2 − 24 x + 7 = 0 16 x 2 − 24 x + 9 − 2 = 0 ( 4 x − 3 ) 2 = 2 4 x − 3 = 2 ∨ 4 x − 3 = − 2 4 x = 3 + 2 ∨ 4 x = 3 − 2 x = 4 3 + 2 ∨ x = 4 3 − 2
To solve the quadratic equation 16 x 2 − 24 x + 7 = 0 , we first calculate the discriminant Δ , which equals 128, indicating two distinct real roots. Using the quadratic formula, we find the solutions to be x 1 = 4 3 + 2 and x 2 = 4 3 − 2 .
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