Answer
$x = 2~~$ or $~~x=5$
Work Step by Step
A quadratic equation can be written in this form:
$ax^2 + bx+c = 0$
where $a,b,$ and $c$ are real numbers and $a \neq 0$
We can determine the values of $a, b,$ and $c$:
$x^2-7x+10 = 0$
$a = 1$
$b = -7$
$c=10$
We can use the quadratic formula to find the solutions of the equation:
$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
$x = \frac{-(-7) \pm \sqrt{(-7)^2-(4)(1)(10)}}{(2)(1)}$
$x = \frac{7 \pm \sqrt{49-40}}{2}$
$x = \frac{7 \pm \sqrt{9}}{2}$
$x = \frac{7 \pm 3}{2}$
$x = \frac{7 - 3}{2}~~$ or $~~x = \frac{7 + 3}{2}$
$x = 2~~$ or $~~x=5$
