consider the following quadratic equation 36x^(2)=49 using the standard form ax^(2)+bx+c=0 of the given quadratic equation factor the left hand side of the equation into two linear factors
To factor the left hand side of the equation, we need to rewrite it in the standard form ax^2 + bx + c = 0.
The given quadratic equation is 36x^2 = 49.
First, let's divide both sides of the equation by 36 to simplify it:
(36x^2) / 36 = 49 / 36
x^2 = 49 / 36
Notice that 49 / 36 is a perfect square. Simplifying further:
x^2 = (7/6)^2
Since (7/6)^2 is a perfect square, we can rewrite it as:
x^2 = (7/6)^2
x^2 - (7/6)^2 = 0
Now, we can factor the left hand side of the equation:
(x - 7/6)(x + 7/6) = 0
So, the left hand side of the equation is factored into two linear factors: (x - 7/6) and (x + 7/6).