Question

The sum of a number and twice its square is 6. Find the number.

Answer 1

      $\underline{\bold{Answer:}}$

      $-2,\frac{3}{2}$

      $\underline{\bold{Step-by-step-explaination:}}$

      $\text{It is given that the sum of a number and twice its square is 6}$

      $\text{Let the number be }x$

$\implies x+ 2x^{2} = 6$

$\implies x+2x^{2} -6 = 0$

$\implies 2x^{2} +x -6 = 0$

      $\text{We can split }x \text{ into }(4x-3x)$

$\implies 2x^{2} +4x - 3x - 6 = 0$

$\implies 2x(x+2) -3(x+2) = 0$

$\implies (x+2)(2x-3)= 0$

$\implies x = -2,\frac{3}{2}$

  $\therefore \text{The number is either }-2 \text{ or }\frac{3}{2}$