Question

Solve $7x^2-30x-25=0$ by completing square method

Answer 1

Given $7x^2-30x-25=0$

$x^2-\frac{30x}{7}-\frac{25}{7}=0$

$\Rightarrow x^2-2\times \frac{15x}{7}+\frac{225}{49}-\frac{25}{7}-\frac{225}{49}=0$

$\Rightarrow (x-\frac{15}{7}{)}^2=\frac{225}{49}+\frac{25}{7}$

$\Rightarrow (x-\frac{15}{7}{)}^2=\frac{225+175}{49}$

$\Rightarrow (x-\frac{15}{7}{)}^2=\frac{400}{49}$

$\therefore x-\frac{15}{7}=\frac{20}{7}$ or $x-\frac{15}{7}=\frac{20}{7}$

$x=\frac{35}{7}$ or $x=\frac{-5}{7}$

$x=5,-5$