Question

What is the solution set of x2 – 10 = 30x?

Answer 1

The solution of the equations are x = 30.33 and x = -0.33 .

Explanation:

As given

x² – 30x - 10 = 0

As the general form of equation is written as

ax² + bx + c = 0

a = 1 , b = -30 ,c= -10

The discriminant form is defined as

`x = \frac{-b\pm\sqrt{b^(2)-4ac}}{2a}`

Put all the values in the discriment formula

`x = \frac{-(-30)\pm\sqrt{(-30)^(2)-4* 1* -10}}{2}`

As

`x = \frac{-(-30)+\sqrt{(-30)^(2)-4* 1* -10}}{2}`

`x = (-(-30)+√(900+40))/(2)`

`x = ((30)+√(940))/(2)`

`x = ((30)+√(940))/(2)`

`√(940) = 30.66`

`x = ((30)+30.66)/(2)`

`x = (60.66)/(2)`

x = 30.33

As

`x = (-(-30)-√(900+40))/(2)`

`x = ((30)-√(940))/(2)`

`x = ((30)-√(940))/(2)`

`√(940) = 30.66`

`x = ((30)-30.66)/(2)`

`x = (-0.66)/(2)`

x = -0.33

Therefore the solution of the equations are x = 30.33 and x = -0.33 .

Answer 2

`x^2 - 30x - 10 = 0 \\ x= \frac{-b \pm \sqrt{ b^(2) -4ac} }{2a}`; where a = 1, b = -30 and c = -10

`x= \frac{-(-30) \pm \sqrt{ (-30)^(2) -4 * 1 * -10} }{2 * 1} \\ = (30 \pm √( 900 +40) )/(2) \\ =(30 \pm √( 940) )/(2) \\ =(30 \pm 2√(235) )/(2) \\ =15+√(235) \ or \ 15-√(235)\\=30.33 \ or \ -0.33`