If (x + 1)(x - 3) = 5, then which of the following statements is true?
x + 1 = 0 or x - 3 = 0
x + 1 = 5 or x - 3 = 5
x - 4 = 0 or x + 2 = 0

Solution:

It is given that

(x + 1)(x - 3) = 5

Using the multiplicative distributive property

x² - 3x + x - 3 = 5

x² - 2x = 5 + 3

x² - 2x = 8

x² - 2x - 8 = 0

For the standard form of a quadratic equation ax² + bx + c = 0

The formula to find the roots is

x = [-b ± √b² - 4ac]/ 2a

In the equation,

a = 1, b = -2 and c = -8

Substituting it we get

x = [-(-2) ± √(-2)² - 4(1)(-8)]/ 2(1)

x = [2 ± √4 + 32]/ 2

x = [2 ± √36]/ 2

x = [2 ± 6]/ 2

So we get

x = (2 + 6)/ 2 = 8/2 = 4

x = (2 - 6)/2 = -4/2 = -2

We can write it as

(x - 4)(x + 2) = 0

Therefore, x - 4 = 0 or x + 2 = 0 is true.

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If (x + 1)(x - 3) = 5, then which of the following statements is true?

Summary:

If (x + 1)(x - 3) = 5, then ,the statement x - 4 = 0 or x + 2 = 0 is true.