Question

x^2+6x+5=0 find the roots of the quadratic equation using completing the square method ​

Answer 1

Answer:

1

Step-by-step explanation:

This quadratic equation lends itself best to factorisation but you specifically asked that it be solved using the square root method. My understanding is the square root method is for a quadratic equation that has no linear term. For example:

x 2  -9 = 0

x 2  = 9

x =  ±   9–√  

x =  ±  3

Are you talking about completing the square method?

x^2 + 6x + 5 = 0

x 2  + 6x + 9 - 9 + 5 = 0

(x + 3) 2  = 4

x+3 =  ±   4–√  

x = -3  ±  2

x = -5 or x = -1

Answer 2

$\underline{\boxed{\bold{ \bigstar \; Question \; \bigstar }}}$  

➠ x² + 6x + 5 = 0 : Find the roots of the quadratic equation using completing the square method ​.

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$\underline{\boxed{\bold{ \bigstar \; Important \; Information \; \bigstar }}}$  

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❏ "Completing Square Method" is one of the most frequently used method to solve quadratic equations.

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❏ Here we add or subtract some terms to make perfect square and then get our answer.

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$\underline{\boxed{\bold{ \bigstar \; Given \; \bigstar }}}$  

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➠ Equation : x² + 6x + 5 = 0

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$\underline{\boxed{\bold{ \bigstar \; Answer \; \bigstar }}}$  

Let's Start !

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❖ Here is your answer :)

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$:\implies x^{2} +6x + 5 = 0$

$:\implies (x^{2} +6x + 5) + 4 - 4= 0$

$:\implies x^{2} +6x +9 - 4= 0$

$:\implies x^{2} +6x +9 = 4$

$:\implies (x+3)^{2} = 4$

$:\implies (x+3)^{2} = 2^{2}$

$:\implies x+3 = \pm 2$

$:\implies x = (\pm 2) - 3$

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$\boxed { \bold { \orange { :\longmapsto x = 2-3 =-1 } } }$

$\boxed { \bold { \orange { :\longmapsto x = -2-3 = -5 } } }$

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$\boxed{\boxed{\bold{\therefore Roots \; of \; Quadratic \; Equation \; are \; (-1) \; and \; (-5)}}}$

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Hope this helps u.../

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