Помогите пожалуйста! -2x^2-7x+19=(x+7)^2. Created by blackcoffeep. matematika-ru

Помогите пожалуйста! -2x^2-7x+19=(x+7)^2...

Verified answer

-2x² - 7x + 19 = (x + 7)²
-2x² - 7x + 19 = x² + 14x + 49
3x² + 21x + 30 = 0
x² + 7x + 10 = 0 D = b²-4ac = 49 - 40 = 9

x₁ = (-b+√D)/2a = (-7+3)/2 = -2
x₂ = (-b -√D)/2a = (-7-3)/2 = -5

Ответ: {-5; -2}

2 votes Thanks 3

oksik1970
$- 2 {x}^{2} - 7x + 19 = {(x + 7)}^{2} \\ - 2 {x}^{2} - 7x + 19 = {x}^{2} + 14x + 49 \\ - 2 {x}^{2} - 7x + 19 - {x}^{2} - 14x - 49= 0 \\ - 3{x}^{2} - 21x - 30 = 0 \\ d = {( - 21)}^{2} - 4 \times ( - 3)\times ( - 30) = 441 - 360 = 81 \\ x1 = \frac{21 + \sqrt{81} }{2 \times ( - 3)} = \frac{21 + 9}{ - 6} = - \frac{30}{6} = - 5 \\ x2 = \frac{21 - \sqrt{81} }{2 \times ( - 3)} = \frac{21 - 9}{ - 6} = \frac{12}{ - 6} = - 2$

1 votes Thanks 1

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