Question

Which of the following equations is equivalent to 7x ^2 - 28x - 33=0 ? a) 7x^2 + 28x - 33 = 0 b) 7x^2 - 33 - 28x = 0

c) 7x^2 - 28x + 33 = 0
d) 7x^2 + 33 - 28x = 0

Answer 1

Final answer:

The equivalent equation is
`\(7x^2 - 28x - 33 = 7(x - (33)/(7))(x + 7) = (7x - 33)(x + 7) = 0\)`,

so the correct option is c)
`\(7x^2 - 28x + 33 = 0\)`.

Step-by-step explanation:

To determine which equation is equivalent to
`\(7x^2 - 28x - 33 = 0\)`, you can factor the quadratic expression. The factored form of a quadratic equation
`\(ax^2 + bx + c\) is \(a(x - r_1)(x - r_2)\)`, where
`\(r_1\)` and
`\(r_2\)` are the roots of the equation.

Factorization:

`\[ 7x^2 - 28x - 33 = 0 \]`

First, find the product of the coefficient of
`\(x^2\)`term (7) and the constant term (-33), which is
`\(-231\)`. Now, look for two numbers whose product is
`\(-231\)` and whose sum is the coefficient of the
`\(x\)` term (-28). These numbers are -33 and +7.

`\[ 7x^2 - 28x - 33 = 7(x - 33/7)(x + 7) \]`

Simplified form:

`\[ (x - 33/7)(7x + 7) = (7x - 33)(x + 7) \]`

So, the equivalent equation is:

`\[ 7x^2 - 28x - 33 = 7(x - 33/7)(x + 7) = (7x - 33)(x + 7) = 0 \]`

Therefore, the correct option is:

c) 7x^2 - 28x + 33 = 0**