Question

Find the roots of the equation $5x^2–6x–2=0$ by the method of completing the square.

• A. $x=\frac{5\pm \sqrt{19}}{3}$
  
• B. $x=\frac{3\pm \sqrt{19}}{5}$​
  
• C. $x=5$
• D. $x=3$

Answer 1

The correct option is B

$x=\frac{3\pm \sqrt{19}}{5}$​

Multiplying the equation throughout by 5, we get

$25x^2–30x–10=0$

This is the same as:

$(5x{)}^2–2\times (5x)\times 3+3^2–3^2–10=0$

$\Rightarrow (5x–3{)}^2–9–10=0$

$\Rightarrow (5x–3{)}^2–19=0$

$\Rightarrow (5x–3{)}^2=19$

$\Rightarrow 5x-3=\pm \sqrt{19}$

$\Rightarrow x=\frac{3\pm \sqrt{19}}{5}$