how do you solve this?

x 2 − 3 x − 4 = 0 x 2 − 2 x ⋅ 2 3 ​ = 4 / + ( 2 3 ​ ) 2 x 2 − 2 x ⋅ 2 3 ​ + ( 2 3 ​ ) 2 = 4 + ( 2 3 ​ ) 2 ( x − 2 3 ​ ) 2 = 4 + 4 9 ​ ( x − 2 3 ​ ) 2 = 4 16 ​ + 4 9 ​ ( x − 2 3 ​ ) 2 = 4 25 ​ x − 2 3 ​ = ± 4 25 ​ ​
x − 2 3 ​ = ± 4 ​ 25 ​ ​ x − 2 3 ​ = ± 2 5 ​ x − 2 3 ​ = − 2 5 ​ or x − 2 3 ​ = 2 5 ​ x = − 2 5 ​ + 2 3 ​ or x = 2 5 ​ + 2 3 ​ x = − 2 2 ​ or x = 2 8 ​ x = − 1 or x = 4

Answered by Anonymous | 2024-06-10

Why not simply factor the left side ?
(x - 4) times (x + 1) = 0
This equation is true if either factor is zero.
(x - 4) = 0 x = 4
(x + 1) = 0 ***x = -1 ***

Answered by AL2006 | 2024-06-10

To solve the quadratic equations, use the quadratic formula t = 2 a − b ± b 2 − 4 a c ​ ​ . For 3 t 2 + t − 4 = 0 , the solutions are t = 1 and t = − 3 4 ​ . Other equations can also be solved similarly, with attention to the discriminant to determine the nature of the roots.
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Answered by Anonymous | 2024-12-24