zomboi
Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

How do I solve a quadratic equation like this: x squared minus 9x = -14?

Sagot :

[tex]x^2-9x=-14\\\\x^2-9x+14=0\\--------------------\\-9=-7+(-2)\\14=-7\cdot(-2)\\--------------------\\\\x^2-9x+14=(x-7)(x-2)\\\\(x-7)(x-2)=0\iff x-7=0\ or\ x-2=0\\\\x=7\ or\ x=2[/tex]



[tex]x^2-9x+14=0\\\\a=1;\ b=-9;\ c=14\\\\\Delta=b^2-4ac\\\\\Delta=(-9)^2-4\cdot1\cdot14=81-56=25\\\\x_1=\frac{-b-\sqrt\Delta}{2a}\to x_1=\frac{9-\sqrt{25}}{2\cdot1}=\frac{9-5}{2}=\frac{4}{2}=2\\\\x_2=\frac{-b+\sqrt\Delta}{2a}\to x_2=\frac{9+\sqrt{25}}{2\cdot1}=\frac{9+5}{2}=\frac{14}{2}=7[/tex]
Bring everything over to one side.
    x² -9x=-14
x²-9x+14=0
Now it is an easy trinomial so you need to find two numbers that add up to -9 and multiply to equal 14. The two numbers are -7 and -2. 
 x²-9x+14=0
 (x-7)(x-2)=0
            x= 7 and 2

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.