2 years ago

3n + 9 = 27 n = ? solve for n

Mathematics

1 answer:

Debora [2.8K]2 years ago

7 0

Answer:

Step-by-step explanation:

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Solve for x.

Ivahew [28]

ANSWER

$x=\frac{2-\sqrt{10}} {3}$

or

$x=\frac{\sqrt{10}+2} {3}$

We have

$3x^2-4x-2=0$

Since we cannot factor easily, we complete the square.

Adding 2 to both sides give,

$3x^2-4x=2$

Dividing through by 3 gives

$x^2-\frac{4}{3}x= \frac{2}{3}$

Adding $(-\frac{2}{3})^2$ to both sides gives

$x^2-\frac{4}{3}x+(-\frac{2}{3})^2= \frac{2}{3}+(-\frac{2}{3})^2$

The expression on the Left Hand side is a perfect square.

$(x-\frac{2}{3})^2= \frac{2}{3}+\frac{4}{9}$

$\Rightarrow (x-\frac{2}{3})^2= \frac{10}{9}$

$\Rightarrow (x-\frac{2}{3})=\pm \sqrt{\frac{10}{9}}$

$\Rightarrow (x)=\frac{2}{3} \pm {\frac{\sqrt{10}}{3}$

Splitting the plus or minus sign gives

$x=\frac{2- \sqrt{10}} {3}$

or

$x=\frac{\sqrt{10}+2} {3}$

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