Question

Solve the equation using the quadratic formula : x^2-10x+25=18

Answer 1

`x^2-10x+25=18 \\ \\x^2-10x+25-18 = 0\\ \\ x^2-10x+ 7 =0 \\ \\a=1 , b = -10 , c= 7 \\ \\ \Delta = b^(2)-4ac = (-10)^(2)-4*1*7=100-28 = 72 \\ \\√(\Delta )=√(72)= √(2*36) =√(36)*√(2) =6√(2)`


`x_(1)=(-b-√(\Delta ))/(2a) =(10- 6√(2))/(2)=(2(5-3√(2)))/(2)= 5-3√(2)\\ \\x_(2)=(-b+√(\Delta ))/(2a) =(10+ 6√(2))/(2)=(2(5+3√(2)))/(2)= 5+3√(2)`



`Answer : \ x= 5-3√(2) \ \ or \ \ x = 5+3√(2)`