Question

What are the roots of the equation x^2 +30x =1000?

Answer 1

Given :-

• x² + 30x = 1000 .

To Find :-

• The roots of the equation .

Solution :-

As we know that if the quadratic equation is in standard form which is ,

`ax^2+bx + c =0`

Then its roots are given by ,

`x =(-b\pm√(b^2-4ac))/(2a)`

So on converting the equation in standard form ,

`x^2+30x -1000=0`

With respect to the standard form ,

• a = 1
• b = 30
• c = -1000

Substitute in the Quadratic formula ,

`x =(-30\pm √((30)^2-4(1)(-1000)))/(2(1))`

Simplify,

`x =(-30\pm√(900+4000))/(2)`

Add the numbers inside square root ,

`x =(-30\pm√(4900))/(2)`

Divide each term in numerator by 2,

`x =(-30)/(2)\pm(√(70^2))/(2)`

Simplify ,

`x = -15 \pm 35`

Separate the two solutions ,

`x = -15 + 35 , -15 -35`

Simplify ,

`x = 20 , -50`

Hence the solution of the equation are 20 and -50 .

I hope this helps.

Answer 2

x=20 and x=-50

Explanation:

To find the roots, we need to simply solve for x. We do this by first moving all of the terms to the left and setting the right side equal to 0.

-1000

x^2+30x-1000=0

Now, factor it.

What adds up to 30 but multiplies to get -1000?

-10 and 40? No, because they multiply to get -400.

-20 and 50? Yes, because they add up to 30 and multiply to get -1000.

(x-20)(x+50)

x-20=0

x=20

x+50=0

x=-50

So, the roots are x=20 and x=-50