- #1
nameVoid
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(1/2)x^4-x^2-1=0
To solve this equation, we will use the method of factoring and the quadratic formula. First, we will factor out a (1/2) from the equation to get (1/2)(x^4-2x^2-2)=0. Then, we can use the quadratic formula to solve for x^2, and then solve for x.
The steps for factoring this equation are as follows:
1. Factor out a (1/2) from the equation to get (1/2)(x^4-2x^2-2)=0.
2. Write the equation in the form of (ax^2+bx+c)(dx^2+ex+f)=0.
3. Use the FOIL method and the distributive property to expand the equation.
4. Group the like terms and factor out common factors.
5. Set each factor equal to 0 and solve for x.
The quadratic formula is x=(-b±√(b^2-4ac))/2a. To use the quadratic formula to solve (1/2)x^4-x^2-1=0, we first need to rewrite the equation in the form of ax^2+bx+c=0. Then, we can plug in the values of a, b, and c into the quadratic formula and solve for x.
Yes, there are a few special cases to consider when solving this equation. One is that the equation has no real solutions if the discriminant (b^2-4ac) is negative. Another is that if the quadratic equation has a single real solution, the discriminant will equal 0. It is also important to note that if the leading coefficient (a) is 0, the equation is no longer quadratic and cannot be solved using the quadratic formula.
Yes, there are other methods that can be used to solve this equation, such as completing the square and graphing. However, factoring and the quadratic formula are the most commonly used methods for solving quadratic equations.