Question

Find the roots of 5x2 – 7x – 6 = 0 by the method of completing the square

Answer 1

AmswEr:-

Given:-

A quadratic equation,

$\tt\longrightarrow5 {x}^{2} - 7x -6 = 0.$

To Find:-

• The roots of the given equation by completing square method.

ID Used:-

$\tt\longrightarrow {a}^{2} - 2ab + {b}^{2} = (a - b) {}^{2} .$

Now, lets find out the roots:-

$\tt\mapsto5 {x}^{2} - 7x - 6 = 0. \\ \\ \tt\mapsto5 {x}^{2} - 7x = 0 + 6. \\ \\ \tt\mapsto5 {x}^{2} - 7x = 6. \\ \\ \tt\mapsto \dfrac{5 {x}^{2} - 7x = 6 }{5} . \\ \\ \rm(dividing \: \: whole \: \: eq \: \: by \: \: 5). \\ \\ \tt\mapsto \dfrac{\cancel5 {x}^{2} }{\cancel5} - \dfrac{7x}{5} = \dfrac{6}{5} . \\ \\ \tt\mapsto {x}^{2} - \dfrac{7x}{5} = \dfrac{6}{5} . \\ \\ \tt\mapsto(x) {}^{2} - 2 \times x \times \dfrac{7}{10} + ( \dfrac{7}{10} ) {}^{2} = \dfrac{6}{5} + ( \dfrac{7}{10} ) {}^{2} . \\ \\ \tt\mapsto(x - \dfrac{7}{10} ) {}^{2} = \dfrac{6}{5} + \dfrac{49}{100} . \\ \\ \tt\mapsto(x - \dfrac{7}{10} ) {}^{2} = \dfrac{120 + 49}{100}. \\ \\ \tt\mapsto(x - \frac{7}{10} ) {}^{2} = \frac{169}{100} . \\ \\ \tt\mapsto(x - \frac{7}{10}) {}^{2} = \frac{ + }{} ( \dfrac{13}{10} ) {}^{2}. \\ \\ \tt\mapsto x - \frac{7}{10} = \frac{ + }{} \: \: \frac{ 13 }{10}. \\ \\ \tt\mapsto x = \frac{ + }{} \: \: \frac{13}{10} + \frac{7}{10} . \\ \\ \tt\mapsto x = \frac{7 + 13}{10} \: \: or \: \: x = \frac{7 - 13}{10} .\\ \\ \tt\mapsto x = \dfrac{\cancel{20}}{\cancel{10}}\:\: Or \:\: x = -\dfrac{\cancel{6}}{\cancel{10}}\\ \\ \mapsto\boxed{\underline{\underline{ \tt x = 2\:\:Or\:\: x=- \frac{3}{5}.}}}$

$\rm\therefore \:The\:\:req\:\:values\:\:x\:\:are\\ \\ \rm 2\:\:Or\:\: -\dfrac{3}{5}.$

Answer 2

Answer:here is your our answer

Step-by-step explanation:

Brainliest please