Factor
72-17v=v^2
First write this quadratic in its general form
v^2 + 17v - 72 = 0
I cannot find any two numbers that have a difference of 17 and multiply to get 72
Secondly, the discriminant value is
17^2-4(1)(-72) = 577
This is not a perfect square, so the equation has irrational roots, which means, that the equation does not factor over the rationals.
v^2 + 17 v -72 = 0
-17 +/- sqrt(289+288)
--------------------
2
= 8.5 +/- 12 approximately
BUT I bet you have a sign error
because if it were
v^2 + 17 v + 72 it would factor into
(v+8)(v+9) = 0
are you sure it is not -72 -17 v = v^2
Thank you. I thought I was loosing my mind.
To factor the given equation, let's move all the terms to one side of the equation to create a quadratic equation.
First, subtract both sides of the equation by 'v^2':
72 - 17v - v^2 = 0
To factor the quadratic equation, we need to find two numbers that multiply to give the product of the constant term (72) and add up to the coefficient of the linear term (-17v).
In this case, the numbers are -8 and -9.
So, we rewrite the equation using these numbers:
(-8)(-9) + (-8)(-v) + (-9)(-v) + v^2 = 0
Simplifying it further:
72 + 8v + 9v + v^2 = 0
Rearranging the terms:
v^2 + 17v + 72 = 0
Now, we can factor the quadratic equation.
Let's find two numbers that multiply to give the product of the coefficient of the square term (1) and the constant term (72) and add up to the coefficient of the linear term (17).
The numbers are 8 and 9.
So, we rewrite the equation using these numbers:
(v + 8)(v + 9) = 0
By applying the zero product property, we can now solve for v:
v + 8 = 0 or v + 9 = 0
Solving these two equations separately:
v = -8 or v = -9
Therefore, the solutions to the equation are v = -8 and v = -9.