Final answer to the problem
$x=-\frac{1}{12}+\sqrt{2}i,\:x=-\frac{1}{12}-\sqrt{2}i$
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Step-by-step Solution
How should I solve this problem?
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- Solve for x
- Find the derivative using the definition
- Solve by quadratic formula (general formula)
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
- Find the roots
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1
Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($-6$) to all terms
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$-6\left(x^2+\frac{1}{6}x-\frac{43}{6}\right)=0$
Learn how to solve problems step by step online. Solve the quadratic equation 43-6x^2-x=0. Use the complete the square method to factor the trinomial of the form ax^2+bx+c. Take common factor a (-6) to all terms. Add and subtract \displaystyle\left(\frac{b}{2a}\right)^2. Factor the perfect square trinomial x^2+\frac{1}{6}x+\frac{1}{144}. Divide both sides of the equation by -6.
Final answer to the problem
$x=-\frac{1}{12}+\sqrt{2}i,\:x=-\frac{1}{12}-\sqrt{2}i$
