Question

Solve the equation by using completing square method: x^2 +4x +5 = 0. Explain every step.

Answer 1

Step 1.)

Transfer the constant term in RHS

=> x^2 + 4x = - 5

Step 2.)

Divide the equation by the coficient of x^2

=> x^2 + 4x = - 5

Step 3.)

Add square of half of the coficient of x in both sides

=> x^2 + 4x + (2)^2 = - 5 + (2)^2

=> ( x + 2)^2 = ( - 5 + 4)

=> ( x + 2) = sqrt ( - 1)

=> x + 2 = + - i

=> x = - 2 +- i

Roots are - 2 + i and - 2 - i

Answer 2

HERE :

A = 1

B = 4

C = 5

USING QUADRATIC EQUATION, WE GET

X = - b + √b^2 -4ac/2a

X = - 4 + √4^2 - 4×1×5/2×1

X = - 4 + √16 - 20/2

X = - 4 + √-4/2

X = - 4 + √4 × i^2/2

X = - 4 + √4 × √i^2/2

X = - 4 + 2 × i/2

X = - 4 + 2i/2

X = - 4 + or - 2i/2