Question

For what value of x is the expression 35 - 18x + 3x2 = 20?

Answer 1

To solve the equation \( 35 - 18x + 3x^2 = 20 \), we first rearrange the terms to set the equation to zero:

\[
3x^2 - 18x + 35 - 20 = 0
\]

This simplifies to:

\[
3x^2 - 18x + 15 = 0
\]

Next, we can divide the entire equation by 3 to simplify it further:

\[
x^2 - 6x + 5 = 0
\]

Now, we can factor the quadratic equation:

\[
(x - 1)(x - 5) = 0
\]

Setting each factor equal to zero gives us the possible solutions:

\[
x - 1 = 0 \quad \Rightarrow \quad x = 1
\]
\[
x - 5 = 0 \quad \Rightarrow \quad x = 5
\]

Thus, the values of \( x \) that satisfy the equation \( 35 - 18x + 3x^2 = 20 \) are:

\[
\boxed{1} \quad \text{and} \quad \boxed{5}
\]