How do you solve $9 x^{2} - 18 x - 1 = 0$ $9x^2 -18x - 1 =0$ by completing the square?

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How do you solve $9 x^{2} - 18 x - 1 = 0$ $9x^2 -18x - 1 =0$ by completing the square?

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Answer 1 · 2016-04-06T12:40:54

The solutions are:
$x = \frac{\sqrt{10} + 3}{3}$ $color(green)(x = (sqrt 10 + 3)/3$ , $x = \frac{- \sqrt{10} + 3}{3}$ $color(green)(x = (-sqrt 10 + 3) / 3$

Explanation:

$9 x^{2} - 18 x - 1 = 0$ $9x^2 - 18x - 1 = 0$

$9 x^{2} - 18 x = 1$ $9x^2 - 18x = 1$

To write the Left Hand Side as a Perfect Square, we add 9 to both sides:

$9 x^{2} - 18 x + 9 = 1 + 9$ $9x^2 - 18x + 9 = 1 + 9$

${(3 x)}^{2} - 2 \cdot 3 x \cdot 3 + 3^{2} = 10$ $(3x)^2 - 2 * 3x * 3 + 3 ^2 = 10$

Using the Identity ${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$ $color(blue)((a-b)^2 = a^2 - 2ab + b^2$ , we get

${(3 x - 3)}^{2} = 10$ $(3x - 3)^2 = 10$

$3 x - 3 = \sqrt{10}$ $3x - 3 = sqrt 10$ or $3 x - 3 = - \sqrt{10}$ $3x - 3 = -sqrt10$

$x = \frac{\sqrt{10} + 3}{3}$ $color(green)(x = (sqrt 10 + 3)/3$ or $x = \frac{- \sqrt{10} + 3}{3}$ $color(green)(x = (-sqrt 10 + 3) / 3$

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How do you solve $9 x^{2} - 18 x - 1 = 0$ $9x^2 -18x - 1 =0$ by completing the square?

1 Answer

Explanation:

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How do you solve $9 x^{2} - 18 x - 1 = 0$ $9x^2 -18x - 1 =0$ by completing the square?