Question

RESOLVA CADA EQUAÇÃO:
A) -3X -9 = -7X - 5
B) (1/2)X -6 = 10
C) X² -7X + 10 = 0
D) -X² + 6x - 9 = 0
E) 2X² - 4X - 8 = 0

Answer 1

Explicação passo-a-passo:

$a) - 3x - 9 = - 7x - 5 \\ - 3x + 7x = - 5 + 9 \\ 4x = 4 \\ x = \frac{4}{4} \\ \\ x = 1$

$b) \frac{x}{2} - 6 = 10 \\ \\ \frac{x}{2} = 10 + 6 \\ \\ \frac{x}{2} = 16 \\ \\ x = 16 \times 2 \\ x = 32$

$c) {x}^{2} - 7x + 10 = 0 \\ x = \frac{ - ( - 7) + - \sqrt{ {( - 7)}^{2} - 4 \times 1 \times 10 } }{2 \times 1} \\ \\ x = \frac{7 + - \sqrt{49 - 40} }{2} \\ \\ x = \frac{7 + - \sqrt{9} }{2} \\ \\ x1 = \frac{7 + 3}{2} = \frac{10}{2} = 5 \\ \\ x2 = \frac{7 - 3}{2} = \frac{4}{2} = 2$

$d) - {x}^{2} + 6x - 9 = 0 \\ x = \frac{ - 6 + - \sqrt{ {6}^{2} - 4 \times ( - 1) \times ( - 9) } }{2 \times ( - 1)} \\ \\ x = \frac{ - 6 + - \sqrt{36 - 36} }{ - 2} \\ \\ x = \frac{ - 6 + - \sqrt{0} }{ - 2} \\ \\ x1 = x2 = \frac{ - 6}{ - 2} = 3$

$e)2 {x}^{2} - 4x - 8 = 0 \\ {x}^{2} - 2x - 4 = 0 \\ x = \frac{ - ( - 2) + - \sqrt{ {( - 2)}^{2} - 4 \times 1 \times ( - 4)} }{2 \times 1} \\ \\ x = \frac{2 + - \sqrt{4 + 16} }{2} \\ \\ x = \frac{2 + - \sqrt{20} }{2} \\ \\ x1 = \frac{2 + 2 \sqrt{5} }{2} = 1 + \sqrt{5} \\ \\ x2 = \frac{2 - 2 \sqrt{5} }{2} = 1 - \sqrt{5}$