solve h(x+5) = 80 as a quadratic

To solve the equation h(x+5) = 80 as a quadratic equation, we first need to remove the parentheses by applying the distributive property. This will give us a quadratic expression that we can then solve for x.

h(x+5) = 80

To remove the parentheses, we need to distribute h to both terms inside the parentheses:

hx + 5h = 80

Now we can rearrange the terms to put the equation in standard quadratic form, which is ax^2 + bx + c = 0:

hx - 80 = -5h

Next, combine like terms:

hx - 5h - 80 = 0

Now, we have a quadratic equation in standard form. We can solve it by factoring, completing the square, or using the quadratic formula.

If factoring is possible, it simplifies the process. However, since the equation has variables (h and x), we cannot guarantee that factoring can be applied effectively. In this case, let's consider using the quadratic formula.

The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Comparing our quadratic equation hx - 5h - 80 = 0 to the standard form ax^2 + bx + c = 0, we can determine the values of a, b, and c:

a = h
b = -5h
c = -80

Now we can substitute these values into the quadratic formula to find the solutions for x:

x = (-(-5h) ± √((-5h)^2 - 4(h)(-80))) / (2h)

Simplifying further:

x = (5h ± √(25h^2 + 320h)) / (2h)

So, the solutions for x are given by the quadratic formula:

x = (5h ± √(25h^2 + 320h)) / (2h)