Question

Find the roots of x square - 4 x minus 8 is equal to zero by the method of completing square

Answer 1

${x}^{2} + 2xy + {y}^{2} = {(x + y)}^{2} \\ {x}^{2} - 4x - 8 = 0 \\ {x}^{2} - 2 \times 2x = 8 \\ adding \: 4 \: on \: both \: sides \\ {x}^{2} - 4x + 4 = 12 \\ {(x - 2)}^{2} = 12 \\ x - 2 = | \sqrt{12} | \\ x = 2 + \sqrt{12} \\ x = 2 - \sqrt{12}$
hope it helps

Answer 2

The roots of the $x=\pm\sqrt{12}+2$

Step-by-step explanation:

Given : Quadratic equation  $x^2-4x-8=0$

To find : The roots of the quadratic equation by the method of completing square ?

Solution :

For a quadratic equation $ax^2+bx+c=0$ the completing square is adding and subtracting half of square of b.

In  $x^2-4x-8=0$ we add and subtract square of 2,

i.e.  $x^2-2\times 2\times x-8+(2)^2-(2)^2=0$

$(x-2)^2-4-8=0$

$(x-2)^2-12=0$

$(x-2)^2=12$

Taking root both side,

$x-2=\pm\sqrt{12}$

$x=\pm\sqrt{12}+2$

Therefore, the roots of the $x=\pm\sqrt{12}+2$

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Find the roots of x square - 4 x minus 8 equal to zero by the method of completing the square​

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