Question

How do you write $21{x^2} + 5x - 35 = 3{x^2} - 4x$in standard form?

Answer 1

Hint: Here we are given equations with the terms on the left hand side of the equation and the terms on the right hand side. We will move all the terms on one side of the equation and then will simplify between the like terms and will convert it in the form of the standard equation, $a{x^2} + bx + c = 0$.

Complete step-by-step solution:
Take the given expression: $21{x^2} + 5x - 35 = 3{x^2} - 4x$
Move all the terms from the right hand side of the equation on the left hand side of the equation. When you move any term from one side to another, the sign of the term also changes. Positive term becomes negative and negative term becomes positive.
$21{x^2} + 5x - 35 - 3{x^2} + 4x = 0$
Rearrange the terms in the above expression, keeping the like terms together. Like terms are the terms having the same variables and its power.
$21{x^2} - 3{x^2} + 5x + 4x - 35 = 0$
Make the pair of like terms together.
$\underline {21{x^2} - 3{x^2}} + \underline {5x + 4x} - 35 = 0$
Simplify the above like terms. When you simplify between two terms, one positive term and one negative term you have to subtract and give a sign of the bigger number.
$18{x^2} + 9x - 35 = 0$
This is the required solution.

Note: While simplification remember the golden rules-
i) Addition of two positive like terms gives the positive term
ii) Addition of one negative and positive like term, you have to do subtraction and give sign of bigger numbers whether positive or negative.
iii) Addition of two negative like terms gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.