Question

solve the following quadratic equation by conpleting square method;
${x}^{2} + 2x - 5 = 0$
​

Answer 1

Answer:

The form for a perfect square is

a

2

+

2

a

b

+

b

2

=

(

a

+

b

)

2

.

x

2

+

2

x

−

5

=

0

.

Add

5

to both sides of the equation.

x

2

+

2

x

=

5

Divide the coefficient of the

x

value by

2

, then square the result.

2

2

=

1

;

1

2

=

1

Add the result to both sides.

x

2

+

2

x

+

1

=

5

+

1

=

x

2

+

2

x

+

1

=

6

The left side is now a perfect square trinomial.

x

2

+

2

x

+

1

=

(

x

+

1

)

2

(

x

+

1

)

2

=

6

Take the square root on both sides.

x

+

1

=

±

√

6

Subtract

1

from both sides.

x

=

√

6

−

1

x

=

−

√

6

−

1