Question

How do you write $ 2{x^2} - 3 = - 6x - 2 $ in standard form?

Answer 1

Hint: Here first of all we will bring all the terms on one side of the equation that is on the left hand side of the equation then will make like terms together and will simplify for the resultant required solution in the form of $ a{x^2} + bx + c = 0 $

Complete step-by-step solution:
Take the given expression.
  $ 2{x^2} - 3 = - 6x - 2 $
Move all the terms from the right hand side of the equation on the left hand side of the equation. Remember when you move any term from one side to the other, signs of the terms are also changed. Positive terms become negative and vice-versa.
  $ 2{x^2} - 3 + 6x + 2 = 0 $
Arrange like terms together in the above equation. Like terms are the terms with the same variable. Also, terms without variables and only constants are also known as the like terms. Constants are the terms having fixed values and it can be any positive or any negative number.
  $ 2{x^2} + 6x\underline { - 3 + 2} = 0 $
Simplify the above equation. When you simplify between one positive term and one negative term, we have to do subtraction and give signs of the bigger number to the resultant value.
  $ 2{x^2} + 6x - 1 = 0 $
The above equation is the required solution.

Note: Always remember while simplification between the like terms, when the sign of both the terms are same you have to do addition and then give sign of the bigger number to the resultant value while if sign of both the terms are different then you have to do subtraction and give sign of bigger digit to the resultant value.