N= -2x^2+76x+430
N = -2(x-43)(x+5)
was there something else you wanted to know about it?
N = -2x + 76 + 430 = 0.
Use Quadratic Formula and get:
X = -5, and X = 43.
The expression you have provided is a quadratic equation in the form of N = -2x^2 + 76x + 430. To find the value(s) of x that satisfy this equation, you have a few different approaches.
1. Factoring: Quadratic equations can sometimes be factored to find their solutions. However, in this case, the given equation does not easily factor, so we need to consider other methods.
2. Quadratic Formula: The quadratic formula can be used to find the solutions of a quadratic equation of the form ax^2 + bx + c = 0. For the given equation (N = -2x^2 + 76x + 430), we can set it equal to zero: -2x^2 + 76x + 430 = 0. Now we can apply the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Comparing with our equation, we have a = -2, b = 76, and c = 430. Plugging these values into the quadratic formula, we have:
x = (-76 ± √(76^2 - 4(-2)(430))) / (2(-2))
Simplifying further:
x = (-76 ± √(5776 + 3440)) / (-4)
x = (-76 ± √(9216)) / (-4)
x = (-76 ± 96) / (-4)
So, we have two possible solutions:
x1 = (-76 + 96) / (-4) = 5
x2 = (-76 - 96) / (-4) = -55
Therefore, the solutions to the equation -2x^2 + 76x + 430 = 0 are x = 5 and x = -55.
3. Graphing: Another way to find the solutions to this equation is by graphing it. You can plot the graph of the equation y = -2x^2 + 76x + 430 and identify the x-intercepts, which represent the solutions to the equation. You can use a graphing calculator or any graphing tool to visualize the equation and find the x-values where the graph intersects the x-axis, which would give the solutions.
These are the different methods you can use to find the solutions for the given quadratic equation.