Question

Resolva a equação:
2x^2=3/2-2x

Answer 1

Resposta:

$x_{1} = \frac{3}{2} \\ x_{2} = - \frac{1}{2}$

Explicação passo-a-passo:

${2x}^{2} = \frac{3}{2} - 2x \\ {2x}^{2} - 2x = \frac{3}{2} \\ 2 \times ( {2x}^{2} - 2x) = 3\\ {4x}^{2} - 4x = 3 \\ {4x}^{2} - 4x - 3 = 0 \\ a = 4 \\ b = - 4 \\ c = - 3 \\ x = \frac{ - ( - 4) + - \sqrt{ {( - 4)}^{2} - 4 \times 4 \times ( - 3) } }{2 \times 4} \\ x = \frac{4 + - \sqrt{16 + 48} }{8} \\ x = \frac{4 + - \sqrt{64} }{8} \\ \\ x_{1} = \frac{4 + 8}{8} = \frac{12 \div 4}{8 \div 4} = \frac{3}{2} \\ x_{2} = \frac{4 - 8}{8} = - \frac{4 \div 4}{8 \div 4} = - \frac{1}{2}$