consider the following quadratic equation 64x^2=40 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 start by rearranging it to the standard form:
64x^2 = 40
Dividing both sides by 64:
x^2 = 40/64
x^2 = 5/8
Now we can factor the left-hand side into two linear factors:
x^2 - 5/8 = 0
Since the coefficient of x^2 is 1, we look for two numbers that multiply to give -5/8 and add up to 0. In this case, there are no such numbers because -5/8 is not factorable into two linear factors with rational coefficients.
Therefore, the left-hand side of the equation cannot be factored into two linear factors. The quadratic equation 64x^2 = 40 is not factorable in the standard form.