quadratic functions

Question

1. Solve (2x + 3)(x − 7) = 15 using two different methods. Describe situations where each might be more advantages or helpful.

Answer 1

(2x + 3)(x − 7) = 15

Before you do anything, make sure the equation is in standard form, ax² + bx + c = 0.

2x² - 14x + 3x - 21 = 15

2x² - 11x - 36 = 0

1.) Using the quadratic formula, we will find the solutions.

Let a = 2, b = -11, and c = -36. Then we have

x = -(-11) ± √(-11)² - 4(2)(-36) / 2(2) = 11 ± √409 / 4 = [-2.306, 7.806]

2.) Use completing the square to find the solutions.

2x² - 11x - 36 = 0

x² - (11/2)x = 18

x² - (11/2)x + (121/16)= 18 + (121/16)

[x - (11/4)]² = (409/16)

x - (11/4) = ± √409/16)

x = (11/4) ± √(409/16) = [-2.306, 7.806]

Answer 2

(2x + 3)(x − 7) = 15

2x^2-14x+3x-21

2x^2-11x=36

x=-2.3.6

I don't know what other way to use. This is the easiest.