x^(2) +6x+9=2

asked Mar 8, 2024 28.0k views

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Hello,

${x}^(2) + 6x + 9 = 2$

$\Leftrightarrow \: {x}^(2) + 6x + 9 - 2 = 0$

$\Leftrightarrow \: x {}^(2) + 6x + 7 = 0$

$\Delta = {b}^(2) - 4ac$

$\Delta = 6 {}^(2) - 4 * 1 * 7 = 36 - 28 = 8 > 0$

$x _(1) = ( - b - √(\Delta) )/(2a) = ( - 6 - √(8) )/(2) = ( - 6 - 2 √(2) )/(2) = - 3 - √(2)$

$x _(2) = ( - b + √(\Delta) )/(2a) = ( - 6 + √(8) )/(2) = ( - 6 + 2 √(2) )/(2) = - 3 + √(2)$

$\boxed{S = { - 3 - √(2) ; \: - 3 + \sqrt[]{2} }}$

Brian Lewis answered Mar 13, 2024

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