4x^2=80x-400
divide each term by 4 and move all terms to the left
x^2 - 20x + 100 = 0
(x - 10)^2 = 0
x-10 = 0
x = 10
To solve the equation 4x^2 = 80x - 400, we can begin by rearranging it into standard form, where one side is equal to zero.
Let's move all the terms to one side:
4x^2 - 80x + 400 = 0
Now, we can simplify the equation by dividing all terms by 4:
x^2 - 20x + 100 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -20, and c = 100. Substituting these values into the quadratic formula, we have:
x = (-(-20) ± √((-20)^2 - 4 * 1 * 100)) / (2 * 1)
Simplifying further:
x = (20 ± √(400 - 400)) / 2
x = (20 ± √0) / 2
Since the square root of 0 is 0, we have:
x = (20 ± 0) / 2
This simplifies to:
x = 20/2 = 10 or x = -20/2 = -10
Therefore, the solutions to the equation 4x^2 = 80x - 400 are x = 10 and x = -10.