Consider the following quadratic equation:
7x^2=15x−2
Step 1 of 2 : Using the standard form ax2+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, let's first put it in standard form:
7x^2 - 15x + 2 = 0
To factor this quadratic equation, we need to find two numbers whose product is equal to the product of the coefficient of the x^2 term (7) and the constant term (2), and whose sum is equal to the coefficient of the x term (-15).
The product of 7 and 2 is 14, so we need to find two numbers that multiply to 14 and add up to -15. The numbers that fit this criteria are -14 and -1.
Now let's rewrite the middle term (-15x) as the sum of -14x and -x:
7x^2 - 14x - x + 2 = 0
Group the terms:
(7x^2 - 14x) + (-x + 2) = 0
Factor out the greatest common factor in each group:
7x(x - 2) - 1(x - 2) = 0
Now we can see that we have a common factor of (x - 2) in both terms. Factor out the common factor:
(x - 2)(7x - 1) = 0
So the left hand side of the equation factors into (x - 2)(7x - 1).