Question

How do you write $ 3{x^2} = 5 - 2x $ in standard form?

Answer 1

Hint: According to the given in the question we have to write the given quadratic expression which is $ 3{x^2} = 5 - 2x $ as mentioned in the question in the standard form. So, to write the expression in the standard form first of all we have to rearrange the terms of the expression which can be done by subtracting with 5 in the both sides of the given expression.
Now, after rearranging the terms of the expression we have to add 2x in the both sides of the given expression.
Now, we write the given quadratic expression we have to equate the expression as y or we can say that we have to write the given expression that y is equal to the given quadratic expression.

Complete step by step answer:
Step 1: First of all we have to rearrange the terms of the expression which can be done by subtracting with 5 in the both sides of the given expression. Hence,
 $ \Rightarrow 3{x^2} - 5 = 5 - 5 - 2x $
Now, we have to solve the expression as obtained just above,
 $ \Rightarrow 3{x^2} - 5 = - 2x $
Step 2: Now, after rearranging the terms of the expression we have to add 2x in the both sides of the given expression. Hence,
 $ \Rightarrow 3{x^2} + 2x - 5 = 2x - 2x $
On solving the expression as obtained just above,
 $ \Rightarrow 3{x^2} + 2x - 5 = 0 $
Step 3: Now, we write the given quadratic expression we have to equate the expression as y or we can say that we have to write the given expression that y is equal to the given quadratic expression. Hence,
 $ \Rightarrow y = 3{x^2} + 2x - 5 $

Hence, we have determined the standard form of the given quadratic expression which is $ y = 3{x^2} + 2x - 5 $ .

Note: To obtain the standard form of the given quadratic expression it is necessary that we have to rearrange all the terms of the expression which can be done by adding or subtracting the terms.
To obtain the standard form of the expression it is necessary that we have to evaluate the obtained expression after rearranging the terms to some variable.