Question

How do you find the x intercepts of $ 36{x^2} + 84x + 49 = 0 $ ?

Answer 1

Hint: For finding the x intercept of the given equation $ 36{x^2} + 84x + 49 = 0 $ which is representing equation of parabola we have equate the equation of parabola with zero, technically when we have an equation in one variable then the equation does not have intercepts; it has a (or more than one) solution(s).

Complete step-by-step answer:
We have , $ 36{x^2} + 84x + 49 = 0 $
We can write this as ,
 $
   36{x^2} = {6x}^2 , {7^2} = 49 , 2(49)(6x) = 84x\;
$
so , it becomes
$
   \Rightarrow {(6x + 7)^2} = 0\\
   \Rightarrow (6x + 7)(6x + 7) = 0 \\
   \Rightarrow 6x + 7 = 0 \\
   \Rightarrow x = - \dfrac{7}{6} \;
  $
Hence we get the solution.
So, the correct answer is “ $ x = - \dfrac{7}{6} $ ”.

Note: The equation for a parabola can also be written in vertex form as $ y = a{(x - h)^2} + k $ where $ (h,k) $ is the vertex of parabola. The point where a parabola has zero gradient is known as the vertex of the parabola. We need to get ‘y’ on one side of the “equals” sign, and all the other numbers on the other side. To solve this equation for a given variable ‘y’, we have to undo the mathematical operations such as addition, subtraction, multiplication, and division that have been done to the variables. Use addition or subtraction properties of equality to gather variable terms on one side of the equation and constant on the other side of the equation. Use the multiplication or division properties of equality to form the coefficient of the variable term equivalent to one.