How do i solve this, by factorizing...
4x(squared)-196=0
Example: 3x(squared)-12=0
(3x+6)(x-2)
THNX
4x(squared)-196=0
4 (x^2-49) = 0
4(x-7)(x+7) = 0
that gives you the answer as x = 7 or x = -7 but if you want it in the rather unusual form you used for the example, multiply out the 4
(4x-28)(x+7) = 0
or (4x + 28)(x-7)
To solve the equation 4x^2 - 196 = 0 by factorizing, we need to find two factors that when multiplied together, result in the equation.
First, we factor out the greatest common factor from the equation, which is 4:
4(x^2 - 49) = 0
By inspecting the remaining expression, we can recognize that it is a difference of squares. Recall that the difference of squares can be factored as (a^2 - b^2) = (a + b)(a - b). In this case, a = x and b = 7:
4(x + 7)(x - 7) = 0
Now, we have a product of three factors equal to zero. According to the zero product property, for a product to be equal to zero, at least one of the factors must be equal to zero. Therefore, we set each factor equal to zero and solve for x:
x + 7 = 0 or x - 7 = 0
Solving these equations gives us two solutions:
x = -7 or x = 7
Therefore, the solutions to the equation 4x^2 - 196 = 0 by factorizing are x = -7 and x = 7.