Final answer to the problem
$y=\left(5-3x^2\right)^7\sqrt{6\left(\left(x+\frac{2}{3}\right)^2-\frac{22}{9}\right)}$
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Step-by-step Solution
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- Differential
- Find the derivative
- Find the integral
- Find the derivative using the definition
- Solve by quadratic formula (general formula)
- Simplify
- Find the integral
- Find the derivative
- Factor
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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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$y=\left(5-3x^2\right)^7\sqrt{6\left(x^2+\frac{4}{3}x-2\right)}$
Learn how to solve equations problems step by step online. Solve the equation y=(5-3x^2)^7(6x^2+8x+-12)^(1/2). 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{4}{3}x+\frac{4}{9}. Simplify the addition \left(x+\frac{2}{3}\right)^2-2-\frac{4}{9}.
Final answer to the problem
$y=\left(5-3x^2\right)^7\sqrt{6\left(\left(x+\frac{2}{3}\right)^2-\frac{22}{9}\right)}$
