Question

8.)Solve x^2 - 10x = -21. O x = 7 and x = 3O x = -7 and x = 3O x = -7 andx = -3O x = 7 and x = -3

Answer 1

x = 7 and x = 3

Explanation

the solution of the quadratic equation

$ax^2+bx+c=0$

is

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

Step 1

$x^2-10x=-21$

a) let the right side equals zero,to do that add 21 in both sides

$\begin{gathered} x^2-10x=-21 \\ add\text{ 21 in both sides} \\ x^2-10x+21=-21+21 \\ x^2-10x+21=0 \end{gathered}$

b)Let

$\begin{gathered} x^2-10x+21=0\Rightarrow ax^2+bx+c=0 \\ hence \\ a=1 \\ b=-10 \\ c=21 \end{gathered}$

now, replace and evaluate to find x

$\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-(-10)\pm\sqrt{(-10^2)-4(1)(21)}}{2(1)} \\ x=\frac{10\pm\sqrt{100-84}}{2}=\frac{10\pm\sqrt{16}}{2} \\ x=\frac{10\pm4}{2} \end{gathered}$

therefore ,t he solutions are

$\begin{gathered} x=\frac{10\pm4}{2} \\ x_1=\frac{10+4}{2}=\frac{14}{2}=7 \\ x_1=\frac{10-4}{2}=\frac{6}{2}=3 \end{gathered}$

so, the answer is

x = 7 and x = 3

I hope this helps you