Question

Resolva a equação: 8x^{2}-14x+3=0

Answer 1

Resposta:

$\boxed{\mathtt{S = \left \{ \frac{3}{2}, \frac{1}{4} \right \}}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{8x^2 - 14x + 3 = 0} \\\\ \mathsf{8x^2 - (12x + 2x) + 3 = 0} \\\\ \mathsf{(8x^2 - 12x) + (- 2x + 3) = 0} \\\\ \mathsf{4x(2x - 3) - 1(2x - 3) = 0} \\\\ \mathsf{(2x - 3) \cdot (4x - 1) = 0}$

Igualando a zero,

FATOR I:

$\\ \displaystyle \mathsf{2x - 3 = 0} \\\\ \boxed{\mathsf{x = \frac{3}{2}}}$

FATOR II:

$\\ \displaystyle \mathsf{4x - 1 = 0} \\\\ \boxed{\mathsf{x = \frac{1}{4}}}$