How do you solve $x^{2} - 2 x - 2 = 0$ $x^2-2x-2=0$ ?

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How do you solve $x^{2} - 2 x - 2 = 0$ $x^2-2x-2=0$ ?

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Answer 1 · 2015-08-06T13:14:47

Use the quadratic formula to get
$XXXX$ $color(white)("XXXX")$ $x = 1 \pm \sqrt{3}$ $x= 1+-sqrt(3)$

Explanation:

For any quadratic equation of the form
$XXXX$ $color(white)("XXXX")$ $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$
the solutions are given by the formula
$XXXX$ $color(white)("XXXX")$ $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x= (-b+-sqrt(b^2-4ac))/(2a)$

Given $x^{2} - 2 x - 2 = 0$ $x^2-2x-2=0$
$a = 1$ $a=1$ $XXXX$ $color(white)("XXXX")$ $b = - 2$ $b=-2$ $XXXX$ $color(white)("XXXX")$ $c = - 2$ $c=-2$
and the quadratic formula gives
$XXXX$ $color(white)("XXXX")$ $x = \frac{2 \pm \sqrt{{(- 2)}^{2} - 4 (1) (- 2)}}{2 (1)}$ $x= (2+-sqrt((-2)^2-4(1)(-2)))/(2(1))$

$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $= \frac{2 \pm \sqrt{12}}{2}$ $= (2+-sqrt(12))/2$

$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $= \frac{2 \pm 2 \sqrt{3}}{2}$ $=(2+-2sqrt(3))/2$

$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $= 1 \pm \sqrt{3}$ $=1+-sqrt(3)$

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How do you solve $x^{2} - 2 x - 2 = 0$ $x^2-2x-2=0$ ?

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