algebra 2 help?

Question

Solve the equation by completing the square.

x^2 - 3x - 15 = -5

Answer 1

Completing the Square

x² - 3x - 15 = - 5

x² - 3x - 15 + 15 = - 5 + 15

x² - 3x = 10

x² - 3x + _____= 10 +______

x² - 3x + 9/4 = 10 + 9/4

(x - 3/2)(x - 3/2) = 40/4 + 9/4

(x - 3/2)² = 49/4

(√x - 3/2)² = ± √49 / √4

x - 3/2 = ± 7/2

x - 3/2 + 3/2 = 3/2 ± 7/2

x = 3/2 ± 7/2

- - - - - - - - - -

Solving for +

x = 3/2 + 7/2

x = 10/2

x = 5

- - - - - - - -

Solving for -

x = 3/2 - 7/2

x = - 4/1

x = - 2

- - - - - - - - -s-

Answer 2

x^2 - 3x - 15 = -5 Need to set the problem equal to zero


x^2 - 3x -10 = 0 We added 5 to both sides


x^2 - 3x -10 = 0 Now we need to know what adds to
-3x and multiplies to -10

x^2 -5x +2x -10 = 0 Then Factor

x(x - 5) 2(x- 5) =0 If both parenthisis are the same then
answer is right.

Answer: (x - 5) (x + 2)
x=5 x=-2

Answer 3

Take the -3. Divide it in half to get -1.5. Square that to get 2.25

x^2 - 3x + 2.25

To get that, you must do the following
x^2 - 3x - 15 + 17.25 = -5 + 17.25
x^2 - 3x +2.25 = 12.25
(x - 1.5)^2 = 12.25
x - 1.5 = +/- sqrt(12.25)
x - 1.5 = +/- 3.5
x = 5 or x = -2

Answer 4

x^2 - 3x - 15 = -5
x^2 -3x +2.25 = -5+15+2.25
(x-1.5)^2 = 12.25
x-1.25 = +/- sqrt(12.25)
x = 1.25 +/- 3.5
x = 4.75 , -2.25