A rectangular pool is 25 feet long and 12 feet wide. If the length is increased by 2x what is the new length? How would you use a quadratic equation to solve this?
Since you indicate no change in width and are only asking for the new length, no quadratic equation needed.
2*25 = ?
I was assuming that 2x = two times. If not,
2x + 25 = ?
Still not a quadratic equation.
To find the new length of the rectangular pool, we need to multiply the original length (25 feet) by 2x and add it to the original length.
So, the new length = original length + (2x * original length).
New length = 25 + (2x * 25).
To solve this using a quadratic equation, we can set up an equation to represent the relationship between the new length and the variable x.
Let's say the new length is represented by L and x is the variable we want to find.
L = 25 + (2x * 25).
To create a quadratic equation, we need to bring all terms to one side and set the equation equal to zero.
L - 25 - 2x * 25 = 0.
Next, we simplify the equation:
L - 25 - 50x = 0.
This equation is now in the form of ax^2 + bx + c = 0, where a = -50, b = -25, and c = L - 25.
We can now solve this quadratic equation using various methods like factoring, completing the square, or the quadratic formula, depending on the specific values of L.
Once we solve the quadratic equation, we will obtain the value of x, which represents the increase in the length.