(x%5E2-3x%2F2-4)%2B10%3D0.jpeg "(x^2-3x/2+3)(x^2-3x/2-4)+10=0")
Solving the Quadratic Equation: (x^2-3x/2+3)(x^2-3x/2-4)+10=0
In this article, we will solve the quadratic equation (x^2-3x/2+3)(x^2-3x/2-4)+10=0. This equation may seem complex at first, but by using algebraic manipulation and factoring, we can simplify it and find the solutions.
Step 1: Expand the Equation
To start, we will expand the equation by multiplying the two binomials:
(x^2 - 3x/2 + 3)(x^2 - 3x/2 - 4) = x^4 - 3x^3/2 - 4x^2 + 9x/2 + 12
Step 2: Simplify the Equation
Next, we will simplify the equation by combining like terms:
x^4 - 3x^3/2 - 4x^2 + 9x/2 + 12 + 10 = 0
Step 3: Rearrange the Equation
Now, we will rearrange the equation to put it in standard quadratic form:
x^4 - 3x^3/2 - 4x^2 + 9x/2 + 22 = 0
Step 4: Factor the Equation (Optional)
At this point, we can try to factor the equation, but it's not possible to factor it easily. Therefore, we will use other methods to solve the equation.
Step 5: Use Numerical Methods or Graphing
Since we cannot factor the equation, we can use numerical methods or graphing to find the solutions. One way to do this is by using a graphing calculator or software to graph the equation and find the x-intercepts.
Conclusion
In conclusion, solving the quadratic equation (x^2-3x/2+3)(x^2-3x/2-4)+10=0 requires patience and persistence. By expanding and simplifying the equation, we can put it in standard quadratic form. Although we cannot factor the equation easily, we can use numerical methods or graphing to find the solutions.
