How do you solve $3 x^{2} - 123 = 0$ $3x^2 - 123 = 0$ ?

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How do you solve $3 x^{2} - 123 = 0$ $3x^2 - 123 = 0$ ?

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Answer 1 · 2016-06-05T09:44:58

$x = \pm \sqrt{41}$ $x=±sqrt41$

Explanation:

The first step is to take out a common factor of 3.

$3 x^{2} - 123 = 0 \Rightarrow 3 (x^{2} - 41) = 0$ $3x^2-123=0rArr3(x^2-41)=0$

now $x^{2} - 41 = 0 \Rightarrow x^{2} = 41$ $x^2-41=0rArrx^2=41$

Taking the 'square root' of both sides

$\Rightarrow \sqrt{x^{2}} = \pm \sqrt{41} \Rightarrow x = \pm \sqrt{41}$ $rArrsqrt(x^2)=±sqrt41rArrx=±sqrt41$

Answer 2 · 2016-06-05T11:38:08

$x = \pm \sqrt{41}$ $x=+-sqrt41$

Explanation:

Isolate $x$ $x$ to find its value

$3 x^{2} - 123 = 0$ $color(blue)(3x^2-123=0$

Add $123$ $123$ both sides

$\to 3 x^{2} - 123 + 123 = 0 + 123$ $rarr3x^2-123+123=0+123$

$\to 3 x^{2} = 123$ $rarr3x^2=123$

Divide both sides by $3$ $3$

$rarr(cancel3x^2)/cancel3=123/3$

$rarrx^2=41$

Take the square root of both sides

And also remember that,when taking the square root of a number,it can be a positive or negative number

Positive or negative - $+-$

$rarrsqrt(x^2)=+-sqrt41$

$color(green)(rArrx=+-sqrt41$

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2 Answers

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