Question

What are the steps to solve-x^2+45=4x

Answer 1

Answer:

$x\text{ = -9 or x = 5}$

Explanation:

Here, we want to solve for the value of x

We start by rearranging the given equation

We have that as:

$\begin{gathered} -x^2+45\text{ = 4x} \\ -x^2-4x+45\text{ = 0} \end{gathered}$

We can use the quadratic formula here

We have that as:

$x\text{ = }\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

where:

a is the coefficient of x^2 which is -1

b is the coefficient of x which is -4

c is the third number which is 45

Substituting the values, we have it that:

$x\text{ = }\frac{4\pm\sqrt{-4^2-4(-1)(45)}}{2(-1)}$$\begin{gathered} x\text{ = }\frac{4\pm\sqrt{16\text{ + 180}}}{-2} \\ \\ x\text{ = }\frac{4\pm\sqrt{196}}{-2} \\ \\ x\text{ = }\frac{4\pm14}{-2} \\ \\ x\text{ = }\frac{4+14}{-2}\text{ or }\frac{4-14}{-2} \\ \\ x\text{ = }\frac{18}{-2}\text{ or }\frac{-10}{-2} \\ \\ x\text{ = -9 or 5} \end{gathered}$