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

Step-by-step explanation

the solution of the quadratic equation

`ax^2+bx+c=0`

is

`x=(-b\pm√(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=(-b\pm√(b^2-4ac))/(2a) \\ x=(-(-10)\pm√((-10^2)-4(1)(21)))/(2(1)) \\ x=(10\pm√(100-84))/(2)=(10\pm√(16))/(2) \\ x=(10\pm4)/(2) \end{gathered}`

therefore ,t he solutions are

`\begin{gathered} x=(10\pm4)/(2) \\ x_1=(10+4)/(2)=(14)/(2)=7 \\ x_1=(10-4)/(2)=(6)/(2)=3 \end{gathered}`

so, the answer is

x = 7 and x = 3

I hope this helps you