2 Answers

Xilliam · Answer 1 · 2022-03-02T03:52:41+0000

Given:

The equation is:

x^2+5x=2

To find:

The solution of the given equation by completing the square.

Solution:

We have,

x^2+5x=2

We need to add the square of half of the coefficient of x on both sides.

Adding
$\left((5)/(2)\right)^2$ on both sides, we get

$x^2+5x+\left((5)/(2)\right)^2=2+\left((5)/(2)\right)^2$

$\left(x+(5)/(2)\right)^2=2+(25)/(4)$

$\left(x+(5)/(2)\right)^2=(8+25)/(4)$

$\left(x+(5)/(2)\right)^2=(33)/(4)$

Taking square root on both sides, we get

$x+(5)/(2)=\pm \sqrt{(33)/(4)}$

$x=\pm (√(33))/(2)-(5)/(2)$

$x=(\pm √(33)-5)/(2)$

x=(√(33)-5)/(2) and
x=(-√(33)-5)/(2)

Therefore, the solutions of the given equation are
and
.

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