MATH SOLVE

4 months ago

Q:
# Solve the quadratic equation by completing the square. verify your answer graphically. (enter your answers as a comma-separated list.) x2 − 4x + 29 = 0

Accepted Solution

A:

Please use " ^ " to indicate exponentiation:

x^2 − 4x + 29 = 0

1) Take HALF of the coefficient (-4) of the x term. That would be -2.

2) SQUARE this result. Answer: 4.

3) Insert this result and its negative inside the equation after "-4x". Result:

x^2 - 4x + 4 - 4 + 29 = 0

4) Rewrite x^2 -4x + 4 as the square of a binomial. Result: (x-2)^2

5) Combine that -4 and that 29: Result: 25. Rewrite:

(x -2)^2 -4 + 29 = 0 as (x-2)^2 + 25 = 0

6) Rewrite (x-2)^2 + 25 = 0 as (x-2)^2 = -25

7) Take the square root of both sides: (x-2) = plus or minus sqrt(-25)

8) Simplify, remembering that the sqrt of -25 is plus or minus i*5 :

x-2 = plus or minus i*5

9) Solve for x:

x = 2 plus or minus i*5

x^2 − 4x + 29 = 0

1) Take HALF of the coefficient (-4) of the x term. That would be -2.

2) SQUARE this result. Answer: 4.

3) Insert this result and its negative inside the equation after "-4x". Result:

x^2 - 4x + 4 - 4 + 29 = 0

4) Rewrite x^2 -4x + 4 as the square of a binomial. Result: (x-2)^2

5) Combine that -4 and that 29: Result: 25. Rewrite:

(x -2)^2 -4 + 29 = 0 as (x-2)^2 + 25 = 0

6) Rewrite (x-2)^2 + 25 = 0 as (x-2)^2 = -25

7) Take the square root of both sides: (x-2) = plus or minus sqrt(-25)

8) Simplify, remembering that the sqrt of -25 is plus or minus i*5 :

x-2 = plus or minus i*5

9) Solve for x:

x = 2 plus or minus i*5