Question

$2 {x}^{2} - 8x = 24$
por favor me ajuda

Answer 1

Boa Tarde

$2x {}^{2} - 8x = 24$

$x {}^{2} - 4x = 12$

$x {}^{2} - 4x - 12 = 0$

$x {}^{2} + 2x - 6x - 12 = 0$

$x \times (x + 2) - 6x - 12 = 0$

$x \times (x + 2) - 6(x + 2) = 0$

$(x + 2) \times (x - 6) = 0$

$x + 2 = 0 \\ x - 6 = 0$

$x = - 2 \\ x - 6 = 0$

$x = - 2 \\ x = 6$

$x_{1} = - 2.x_{2} = 6$

Espero ter ajudado e bons estudos ✔

Answer 2

Olá Gabriel!

$\\ \displaystyle \mathsf{2x^2 - 8x = 24} \\\\ \mathsf{2x^2 - 8x - 24 = 0 \qquad \qquad \div(2} \\\\ \mathsf{x^2 - 4x - 12 = 0}$

Por conseguinte, devemos determinar o valor do discriminante (Delta), onde a = 1, b = - 4 e c = - 12.

$\\ \displaystyle \mathsf{\Delta = b^2 - 4ac} \\\\ \mathsf{\Delta = (- 4)^2 - 4 \cdot (1) \cdot (- 12)} \\\\ \mathsf{\Delta = 16 + 48} \\\\ \mathsf{\Delta = 64}$

Por fim,

$\\ \displaystyle \mathsf{x = \frac{- b \pm \sqrt{\Delta}}{2a}} \\\\\\ \mathsf{x = \frac{- (- 4) \pm \sqrt{64}}{2 \cdot 1}} \\\\\\ \mathsf{x = \frac{4 \pm 8}{2}}$

$\\ \displaystyle \mathsf{\bullet \qquad x_1 = \frac{4 + 8}{2} = \frac{12}{2} \Rightarrow \boxed{\mathsf{x_1 = 6}}} \\\\\\ \mathsf{\bullet \qquad x_2 = \frac{4 - 8}{2} = \frac{- 4}{2} \Rightarrow \boxed{\mathsf{x_2 = - 2}}}$

Logo, $\boxed{\boxed{\mathsf{S = \left \{ - 2, 6 \right \}}}}$.