## Final Answer

## Step-by-step explanation

Problem to solve:

Moving the term $-10$ to the other side of the equation with opposite sign

Factor the polynomial $-x^2+7x$ by it's GCF: $x$

Divide both sides of the equation by $x$

Grouping terms

Moving the term $7$ to the other side of the equation with opposite sign

Combine $-x+\frac{-10}{x}$ in a single fraction

When multiplying two powers that have the same base ($x$), you can add the exponents

Multiply both sides of the equation by $x$

We need to isolate the dependent variable $x$, we can do that by subtracting $-10$ from both sides of the equation

Multiplying both sides of the equation by $-1$

Grouping terms

Factor the polynomial $x^2-7x$ by it's GCF: $x$

Divide both sides of the equation by $x$

Grouping terms

Moving the term $-7$ to the other side of the equation with opposite sign

Combine $x+\frac{10}{x}$ in a single fraction

When multiplying two powers that have the same base ($x$), you can add the exponents

Multiply both sides of the equation by $x$

Grouping terms

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=-7$ and $c=10$. Then substitute the values of the coefficients of the equation in the quadratic formula:

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

To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)

Subtract the values $7$ and $-3$

Add the values $7$ and $3$

Divide $10$ by $2$

Divide $4$ by $2$