Question

When A = 200, solve the equation x2 - 40x + A=0 using the quadratic formula. Show all your working and give your answers correct to 2 decimal places.​

Answer 1

Solution given:

equation is:

x²-40x+A=0

when A=200

equation becomes

x²-40x+200=0

Comparing above equation with ax²+bx+c=0 we get

a=1

b=-40

c=200

By using quadratic equation formula

x=
`\displaystyle (-b±√(b²-4ac))/(2a)`

substituting value

x=
`\displaystyle (-*-40±√((-40)²-4*1*200))/(2*1)`

x=
`\displaystyle (40±√(800))/(2)`

x=
`\displaystyle (40±20√(2))/(2)`

taking positive

x=
`\displaystyle (40+20√(2))/(2)`

x=34.14

taking negative

x=
`\displaystyle (40-20√(2))/(2)`

x=5.86

x=34.14 or 5.86