Question

5x^2-2x-10=0 find roots the method of completing the square​

Answer 1

Answer:

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Answer 2

Answer:

The roots of the equation 5x²-2x-10=0 are  $x=\frac{1-\sqrt{51} }{5},x=\frac{1+\sqrt{51} }{5}$

Step-by-step explanation:

Given equation is 5x²-2x-10=0

Required to find the roots of the equation by completing the squares

Solution

5x²-2x-10=0 ⇒ $\frac{5x^2-2x-10}{5}$ = 0

⇒ $x^2-\frac{2}{5} x-2}{$ = 0

⇒ $x^2-\frac{2}{5} x + (\frac{1}{5})^2 - (\frac{1}{5})^2 -2}{$ = 0

⇒ $x^2-\frac{2}{5} x + (\frac{1}{5})^2 -\frac{1}{25} - 2}{$ = 0

⇒ $(x-\frac{1}{5})^2 -(\frac{1}{25} + 2})$ = 0

⇒ $(x-\frac{1}{5})^2 -(\frac{1}{25} + 2})$ = 0

⇒ $(x-\frac{1}{5})^2 -(\frac{51}{25})$ = 0

⇒ $(x-\frac{1}{5})^2 -(\frac{51}{25})$ = 0

⇒ $(x-\frac{1}{5})^2 -(\frac{\sqrt{51} }{5})^2$ = 0

⇒ $((x-\frac{1}{5})+(\frac{\sqrt{51} }{5}))((x-\frac{1}{5})-(\frac{\sqrt{51} }{5}))$ = 0

⇒ $(x-(\frac{1-\sqrt{51} }{5})(x-(\frac{1+\sqrt{51} }{5})$ = 0

⇒ $x=\frac{1-\sqrt{51} }{5},x=\frac{1+\sqrt{51} }{5}$

Hence the roots of the equation 5x²-2x-10=0 are $x=\frac{1-\sqrt{51} }{5},x=\frac{1+\sqrt{51} }{5}$

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