Question

Solve $5x^2-6x-2=0$

• A. $x=\frac{3}{5}\pm \frac{\sqrt{1}9}{25}$
• B. $x=\frac{2}{5}\pm \frac{\sqrt{1}9}{5}$
• C. $x=\frac{3}{5}\pm \frac{\sqrt{1}9}{5}$
• D. $x=\frac{3}{5}\pm \frac{\sqrt{1}7}{5}$

Answer 1

The correct option is C $x=\frac{3}{5}\pm \frac{\sqrt{1}9}{5}$

In the equation, $5x^2-6x-2=0$

a = 5, b = -6 and c= -2. Divide by 5 to reduce it to standard form.

$\frac{5x^2-6x-2}{5}=0$

$x^2-\frac{6}{5}x-\frac{2}{5}=0$

Add and subtract $(\frac{3}{5}{)}^2$ to complete the squares,

$x^2-\frac{6}{5}x-\frac{2}{5}+(\frac{3}{5}{)}^2-(\frac{3}{5}{)}^2=0$

$x^2-2\times x\times \frac{3}{5}x+(\frac{3}{5}{)}^2-(\frac{3}{5}{)}^2-\frac{2}{5}=0$

$(x-\frac{3}{5}{)}^2-(\frac{3}{5}{)}^2-\frac{2}{5}=0$

On completing the squares,

$(x-\frac{3}{5}{)}^2=\frac{19}{25}$

Taking square root on both sides,
$(x-\frac{3}{5})=\pm \frac{\sqrt{1}9}{5}$

Thus, the roots of $5x^2-6x-2=0$ are

$x=\frac{3}{5}\pm \frac{\sqrt{1}9}{5}$