Question

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

Answer 1

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

Answer 2

`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`




`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=(-b-\sqrt\Delta)/(2a)\to x_1=(9-√(25))/(2\cdot1)=(9-5)/(2)=(4)/(2)=2\\\\x_2=(-b+\sqrt\Delta)/(2a)\to x_2=(9+√(25))/(2\cdot1)=(9+5)/(2)=(14)/(2)=7`