Find the equation, complete the square, factor

Question

I would like to see how these problems are supposed to be worked out because I went wrong somewhere while solving.

 

1. Find the equation of a line through the point (2,-3) that is parallel to the line with equation 2x+3y-5=0. Express the equation in slope intercept form.

 

2. Solve by completing the square. x^2-4x-14=0

 

3. Factor the expression completely. 2x^3-5x^2-6x+15

Answer 1

2x+3y-5=0    Solve for y.

3y = -2x + 5

y = (-2/3)x + 5/3     The slope of this line is -2/3. Since parallel lines have the same slope, the slope of the new line would also be -2/3. Now use the point-slope form for the equation for a line: y-y₁ = m(x-x₁)

y+3 = (-2/3)(x-2)

y+3 = (-2/3)x + 4/3

y = (-2/3)x - 5/3

 

x² - 4x = 14

x² - 4x + 4 = 14 + 4

(X-2)² = 18      Take the square root of both sides.

x-2 = √18

x = 3√2 +2

 

2x³ - 5x² - 6x + 15 = 

(2x³ - 5x²) - (6x -15) = 

x²(2x-5) - 3(2x-5) = 

(2x-5)(x²-3)