Question

What is the converted form of the equation 5$x^2$ – 6$x$ – 2 = 0 after completing the square by the method of completion of the square?

• A. (5x - 3)² – 19 = 0
• B. (5x - 3)² + 19 = 0
• C. (5x + 3)² – 19 = 0
• D. (5x+3)² + 19 = 0

Answer 1

The correct option is A

(5x - 3)² – 19 = 0

Multiplying the equation throughout by 5, we get

25$x^2$– 30$x$ – 10= 0

This is the same as

$\Rightarrow$ ${\left(5x\right)}^2$ - 2$\times$(5$x$)$\times$3 + $3^2$ - $3^2$ - 10 = 0

$\Rightarrow$ ${(5x-3)}^2$ - 9 - 10 = 0

$\Rightarrow$${(5x-3)}^2$ - 19 = 0