56 over X = 9-X over 2
Can someone tell me what X is please :) Thankyou for your help. If you don't want to just tell me the answer, it would be great if you could give a step-by-step example of how to do one similar to that. or an example of how to do the one I can't do. (Above)
To solve the equation 56/X = (9-X)/2 for X, we can follow these steps:
Step 1: Cross multiply the equation.
Multiply both sides of the equation by the denominators to eliminate the fractions. This will give us:
2 * (56/X) = X * (9-X)
Step 2: Simplify the equation.
Simplify both sides of the equation:
112/X = 9X - X^2
Step 3: Rearrange the equation.
Move all terms to one side of the equation in descending order of the variable:
X^2 + 9X - 112/X = 0
Step 4: Multiply through by X to remove the fraction.
This will yield a quadratic equation:
X^3 + 9X^2 - 112 = 0
Step 5: Solve the quadratic equation.
To solve this quadratic equation, you can use various methods such as factoring, completing the square, or using the quadratic formula. The quadratic equation can be factored as follows:
(X + 16)(X - 7)(X + 1) = 0
Step 6: Determine the value of X.
Since we have three factors equal to zero, we can set each factor to zero and solve for X:
X + 16 = 0
X - 7 = 0
X + 1 = 0
Solving each equation:
1) X + 16 = 0
X = -16
2) X - 7 = 0
X = 7
3) X + 1 = 0
X = -1
Therefore, the values of X that satisfy the equation 56/X = (9-X)/2 are X = -16, X = 7, and X = -1.