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

Apr 20, 2016

x = -6 , x = 5

#### Explanation:

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

$\Rightarrow 2 {x}^{2} + 2 x - 60 = 0$

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

hence: $2 \left({x}^{2} + x - 30\right) = 0$

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 ${x}^{2} + x - 30 = \left(x + 6\right) \left(x - 5\right)$

$\Rightarrow 2 \left(x + 6\right) \left(x - 5\right) = 0 \text{ has to be solved }$

Now 2 ≠ 0

solve (x + 6) = 0 → x = -6

and solving (x - 5) = 0 → x = 5

solutions are $\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{x = - 6 \mathmr{and} x = 5} \textcolor{w h i t e}{\frac{a}{a}} |}}}$