14z^2+81z-9
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(a-3)(a+7)=-9
To simplify the expression 14z^2 + 81z - 9, we can apply the quadratic formula or factor it if possible.
Method 1: Factoring
To determine if the expression is factorable, we need to find two numbers that multiply to give -126 (14 * -9) and add up to 81. Since 126 is not a perfect square, we can't use whole numbers.
Therefore, we move to method 2: Quadratic Formula.
Method 2: Quadratic Formula
The quadratic formula can be used to solve any quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.
For the equation 14z^2 + 81z - 9, we have:
a = 14, b = 81, and c = -9.
The quadratic formula is given by:
z = (-b ± √(b^2 - 4ac)) / (2a)
Applying the formula to our equation, we get:
z = (-81 ± √(81^2 - 4 * 14 * -9)) / (2 * 14)
Simplifying this expression will give us the solutions for z.