Question

solve the given equation x²+4×-5=0 by completing square method​

Answer 1

Solution

Find :-

• Solution of given equation by Complete square method x² + 4x - 5 = 0

Explanation

For this Solution , we follow some steps

Steps(1).

Keep Constant part in R.H.S.

==> x² + 4x = 5

Steps(2).

For Complete Square of L.H.S. add 4 in both sides

==> x² + 2 * x * 2 + 4 = 5 + 4

==> x² + 2*x*2 + 2² = 9

Using Formula

★ ( a + b)² = a² + b² + 2ab

So,

==> (x + 2)² = 9

==> (x + 2) = ±√9

==> x = ±√9 - 2

For ,Solution Take first (-ve) sign

==> x = -√9 - 2

==>x = -3 - 2 [ √9 = 3]

==> x = -5

Again, now take +ve sign

==> x = √9 - 2

==> x = 3 - 2

==> x = 1

Hence

• Solution of give equation will be = -5 & 1

_________________

Answer 2

$\bold{x^2+4x-5=0}\\\\\rightarrow \bold{x^2+2.x.2-5=0\; [\;\;\;So,b=2\;\;]}$

Now add and subtract 4 i.e., 2².

$\rightarrow \bold{x^2+2.x.2+2^2-2^2-5=0}\\\\\rightarrow \bold{(x+2)^2=5+4}\\\\\rightarrow \bold{(x+2)^2=9}\\\\\rightarrow \bold{x+2=\pm \; 3}\\\\\rightarrow \bold{x=-\;2\;\pm \; 3}\\\\\rightarrow \bold{x=-2+3 \;\;\&\;\; x=-2-3}\\\\\rightarrow \bold{\bf{\blue{x=1\;\;\;\&\;\;\;x=-5}}}$

So , solution of the given equation x² + 4x - 5 = 0 is x = -5 , 1