What are the solutions to the equation 2(x^2+x-11)^(3)/(2)=54 ? x= and square

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What are the solutions to the equation 2(x^2+x-11)^(3)/(2)=54 ? x= and square

Answer 1

To solve the equation, follow these steps:1. Divide both sides of the equation by 2 to isolate the term on the left side: \(\left(x^{2}+x-11\right)^{\frac{3}{2}} = 27\)2. Take the cube root of both sides to remove the exponent of 3/2: \(x^{2}+x-11 = \sqrt[3]{27}\) \(x^{2}+x-11 = 3\)3. Rearrange the equation to set it equal to zero: \(x^{2}+x-14 = 0\)4. Factor the quadratic equation: \((x-3)(x+4) = 0\)5. Set each factor equal to zero and solve for x: \(x-3 = 0\) --> \(x = 3\) \(x+4 = 0\) --> \(x = -4\)So, the solutions to the equation are \(x = 3\) and \(x = -4\).

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What are the solutions to the equation 2(x^2+x-11)^(3)/(2)=54 ? x= and square

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