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How do you solve $x^{2} + 2 x = 3$ $x^2+2x=3$ ?

1 Answer

Jun 28, 2016

$x = - 3$ $x=-3$ or $x = 1$ $x=1$

Explanation:

$x^{2} + 2 x = 3$ $x^2+2x=3$

Implies
$XXX x^{2} + 2 x - 3 = 0$ $color(white)("XXX")x^2+2x-3=0$

which can be factored as
$XXX (x + 3) (x - 1) = 0$ $color(white)("XXX")(x+3)(x-1)=0$

which, in turn, implies
either
$XXX x + 3 = 0 XX \to XX x = - 3$ $color(white)("XXX")x+3=0 color(white)("XX")rarrcolor(white)("XX")x=-3$
or
$XXX x - 1 = 0 XX \to XX x = 1$ $color(white)("XXX")x-1=0 color(white)("XX")rarrcolor(white)("XX")x=1$

(As always you should substitute these values into the original equation to verify the result).

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