Solving the Equation: 10/25 - x^2 - 1/5 + x - x/x - 5 = 0
In this article, we will explore the solution to the equation 10/25 - x^2 - 1/5 + x - x/x - 5 = 0.
Simplifying the Equation
Let's start by simplifying the equation. We can begin by combining the fractions:
10/25 = 2/5
So, the equation becomes:
2/5 - x^2 - 1/5 + x - x/x - 5 = 0
Next, we can simplify the fraction -x/x to 1, since any number divided by itself is equal to 1.
The equation now becomes:
2/5 - x^2 - 1/5 + x - 1 - 5 = 0
Rearranging the Equation
Let's rearrange the equation to make it easier to solve. We can start by combining the constants:
-5 - 1 = -6
So, the equation becomes:
2/5 - x^2 - 1/5 + x - 6 = 0
Next, we can multiply both sides of the equation by 5 to eliminate the fractions:
10 - 5x^2 - 1 + 5x - 30 = 0
This simplifies to:
-5x^2 + 5x - 21 = 0
Factoring the Equation
Now, we can try to factor the equation:
-5x^2 + 5x - 21 = -(5x^2 - 5x + 21) = 0
Unfortunately, this equation does not factor easily. Therefore, we will need to use other methods to solve it.
Solving the Equation
One way to solve this equation is by using the quadratic formula. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = -5, b = 5, and c = -21. Plugging these values into the formula, we get:
x = (-(5) ± √((5)^2 - 4(-5)(-21))) / 2(-5) x = (-5 ± √(25 + 420)) / -10 x = (-5 ± √445) / -10
Simplifying this expression, we get:
x = (-5 ± 21.02) / -10
x = 0.5 or x = -4.202
Therefore, the solutions to the equation 10/25 - x^2 - 1/5 + x - x/x - 5 = 0 are x = 0.5 and x = -4.202.
Conclusion
In this article, we have successfully solved the equation 10/25 - x^2 - 1/5 + x - x/x - 5 = 0 using algebraic manipulations and the quadratic formula. The solutions to the equation are x = 0.5 and x = -4.202.
