"Solve with quadratic formula"Solve with quadratic formula
5x^2 - 10x = 7x^2 + 17 5x2−10x=7x2+17
"Subtract 7x^2 + 17 from both sides"Subtract 7x^2 + 17 from both sides
5x^2 - 10x - (7x^2 + 17) = 7x^2 + 17 - (7x^2 + 17)5x2−10x−(7x2+17)=7x2+17−(7x2+17)
"Refine"Refine
-2x^2 - 10x - 17 = 0−2x2−10x−17=0
"Quadratic Equation Formula"Quadratic Equation Formula
x_1,2 = {-b± sqrt (b^2 - 4"ac")}/"2a"x1,2=−b±√b2−4ac2a
a = -2, b = -10, c = -17: a=−2,b=−10,c=−17:
x_1,2 = {-(-10) ± sqrt (-10^2 - 4(-2)(-17))}/"2(-2)"x1,2=−(−10)±√−102−4(−2)(−17)2(-2)
x_1,2 = {-(-10) + sqrt (-10^2 - 4(-2)(-17))}/"2(-2)" = -5/2 - i3/2x1,2=−(−10)+√−102−4(−2)(−17)2(-2)=−52−i32
x_1,2 = {-(-10) - sqrt (-10^2 - 4(-2)(-17))}/"2(-2)"= -5/2 + i3/2x1,2=−(−10)−√−102−4(−2)(−17)2(-2)=−52+i32
x = -5/2 - i3/2x=−52−i32, x = -5/2 -i3/2x=−52−i32
