Solve by completing the square:?

Question

x^2+8x+13=0

Thank you so much for the help

Answer 1

Completing the square

x² + 8x + 13 = 0

Transpose 13

x² + 8x + 13 - 13 = 0 - 13

x² + 8x = - 13

x² + 8x +_____ = 13 +_____

Divide 8 by 2 equals 4. Then square 4 equals 16

Insert 16 in the blank section

x² + 8x + 16 = - 13 + 16

You have a perfect square on the left side of the equation.

(x + 4)(x + 4) = 3

(x + 4)² = 3

Square root on both sides of the equation

(√x + 4)² = ± √3

x + 4 = ± √3

Transpose 4

x + 4 - 4 = - 4 ± √3

x = - 4 ± √3

x = - 4 ± 1.7320050808
- - - - - - - -

Solving for +

x = - 4 + 1.732050808

x = - 2.267949192

- - - - - -

Solving for -

x = - 4 - 1.732050808

x = - 5.732050808

- - - - - - - s-

Answer 2

to complete the square, move the 13 to right side by subtraction

x^2 + 8x = -13

complete the square on the x side by taking ((1/2)8)^2= 4^2 = 16
add 16 to both sides

x^2 + 8x + 16 = -13 + 16

Factor the left
(x + 4)^2 = 3

take the square root

x + 4 = +/- sqrt 3

x = -4 +/- sqrt3

Answer 3

(x ² + 8 x + 16) - 16 + 13 = 0
(x + 4) ² = 3
(x + 4) = ± √3
x = - 4 ± √3

Answer 4

X = -3

Answer 5

you have to use the quadratic formula

X = -b +/- the square root of b squared - 4 times a and c......all over 2 times a

in your problem the a is the coefficient of x squared or 1
the b is the 8 and the c is 13

so your answer should be negative 4 plus or minus the square root of 3