24/(x+1) + 12/(4-x) = 14
Multiply both sides by (4-x)(x+1)
24(4-x) + 12(x+1) = 14(4-x)(x+1)
96 - 12x + 12 = -14(x^2 -3x -4)
= -14x^2 +42 x +56
Combine terms and solve for x.
sorry guys, here's another.I'm not the greatest at math but i do know some...
The rectangle given has a perimeter of 14 units. Find the value(s) of x by factoring a quadriatic equation.
one side= 12/(x+1)
other side= 6/(4-x)
thanks for your help.
To solve this problem, we can start by setting up equations for the length and width of the rectangle.
Let's say the length of the rectangle is x units, and the width is y units. The perimeter of a rectangle is calculated by adding up the lengths of all sides, which in this case would be:
2x + 2y = 14
Now, let's substitute the expressions given for the sides of the rectangle into the equation:
2 * (12/(x+1)) + 2 * (6/(4-x)) = 14
Simplifying further:
24/(x+1) + 12/(4-x) = 14
To solve this equation, we can multiply both sides by the common denominator, which is (x+1)(4-x):
(x+1)(4-x) * (24/(x+1) + 12/(4-x)) = (x+1)(4-x) * 14
This allows us to eliminate the denominators:
24(4-x) + 12(x+1) = 14(x+1)(4-x)
Expanding both sides:
96 - 24x + 12 + 12x = 56(x+1) - 14(x+1)(x-4)
Combining like terms:
108 - 12x = 56x + 56 -14(x^2 - 3x - 4)
Simplifying:
108 - 12x = 56x + 56 -14x^2 + 42x + 56
Rearranging the equation to form a quadratic equation:
-14x^2 + 98x + 168 = 0
Now, we can solve this quadratic equation by factoring or by using the quadratic formula.
To factor, we try to find two numbers whose product is -14 * 168 = -2352 and whose sum is 98. After some trial and error, we find that the numbers are -42 and 56.
Therefore, we can rewrite the equation as:
(-14x - 42)(x - 56) = 0
Setting each factor equal to zero:
-14x - 42 = 0 or x - 56 = 0
Solving each equation separately:
-14x = 42 or x = 56
Dividing both sides by -14, we get:
x = -3 or x = 56
So, the possible values of x for this problem are -3 and 56.