Consider the following quadratic equation:
21x^2=11x+40
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, we need to write 21x^2 as the product of two linear factors.
Let's find the two numbers whose product is 21 and whose sum is the coefficient of the x-term, which is 11. These numbers are 7 and 3.
So, we can rewrite the equation as:
(7x + ___)(3x + ___) = 11x + 40
Now, we need to find the values to fill in the blanks.
To find the first value, we multiply the coefficient of x in the first binomial, which is 7, by the constant term in the second binomial, which is 40.
7 * 40 = 280
Now, we need to find two numbers whose product is 280 and whose sum is the coefficient of x, which is 11. These numbers are 20 and 14.
So, we can rewrite the equation as:
(7x + 20)(3x + 14) = 11x + 40
Therefore, the left hand side of the equation can be factored into two linear factors as (7x + 20)(3x + 14).