Question

How do you solve `2x^2 + 2x = 60`?

Answer 1

x = -6 , x = 5

Explanation:

Since this is a quadratic equation, we wish to equate the terms to zero , before solving.

`rArr 2x^2 + 2x - 60 = 0`

and to solve , we must factorise, remove a common factor of 2.

hence: `2(x^2 + x - 30) = 0`

To factor the quadratic , look for 2 factors which multiply to -30 and sum to 1 ( the coefficient of the x-term).

These are +6 and - 5

thus `x^2 + x - 30 = (x + 6)(x - 5)`

`rArr 2(x + 6)(x - 5 ) = 0 " has to be solved "`

Now 2 ≠ 0

solve (x + 6) = 0 → x = -6

and solving (x - 5) = 0 → x = 5

solutions are `color(red)(|bar(ul(color(white)(a/a)color(black)( x = - 6 and x = 5 )color(white)(a/a)|)))`