solve the quadratic equation by completing the square. Provide the exact and decimal approximation solution

Question

1.)  x²-4x+1=22                                      2.) x²+16x+4=0

Answer 1

completing the square

 

x^2-4x+1=22

x^2-4x    =21

-4/2=-2, (-2)^2=4

x^2-4x+4=21+4

(x-2)^2=25

take the square root of both sides

x-2=+5

x=2+5

x=7 and x=-3

 

x^2+16x+4=0

x^2+16x    =-4

16/2=8, 8^2=64

x^2+16x+64=64-4

(x+8)^2=60

take the square root of both sides

x+8=+√60

x+8=+2√15

x=-8+2√15

x=-8+2√15, x=-8+2(3.872980)=-8+7.74596=-0.25404

X=-8-2√15, X=-8-7.74596=-15.74596

Answer 2

1.) x2-4x+1=22

Factorizing we have (x - 7)*(x + 3) => x1 = 7 ; x2 = -3

2.) x2+16x+4=0

solving for x we have applying the quadratic equation; x1 = (-16 + 15.49)/2 = -0.25

x2 = -15.75