Question

Create a function graph to answer the question. What are the solutions x^2 -5x= -4 enter the smallest value first

Answer 1

To solve the equation \(x^2 - 5x = -4\), we first rearrange it into standard form:

\[
x^2 - 5x + 4 = 0
\]

Next, we can factor the quadratic equation. We are looking for two numbers that multiply to \(4\) (the constant term) and add up to \(-5\) (the coefficient of \(x\)).

The numbers that satisfy this are \(-4\) and \(-1\). Thus, we can factor the equation as follows:

\[
(x - 4)(x - 1) = 0
\]

Setting each factor to zero gives us the solutions:

\[
x - 4 = 0 \quad \Rightarrow \quad x = 4
\]

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

Thus, the solutions to the equation \(x^2 - 5x = -4\) are \(x = 1\) and \(x = 4\).

When entering the smallest value first, the solutions can be stated as:

\[
x = 1, 4
\]

If you need additional assistance with graphing the function \(f(x) = x^2 - 5x + 4\) to visualize these solutions, please let me know!