Solve the equation: 2(x^(2)+x-11)^(3//2)=54

Isolate term with exponent: Divide both sides of the equation by 2 to isolate the term with the exponent. 2(x^2 + x - 11)^(3/2) = 54 (x^2 + x - 11)^(3/2) = 54 / 2 (x^2 + x - 11)^(3/2) = 27Remove exponent: Take the reciprocal of the exponent (2/3) to both sides to remove the exponent on the left side. [(x^2 + x - 11)^(3/2)]^(2/3) = 27^(2/3) x^2 + x - 11 = 27^(2/3)Calculate value: Calculate the value of 27^(2/3). 27^(2/3) = (3^3)^(2/3) 27^(2/3) = 3^(3*(2/3)) 27^(2/3) = 3^2 27^(2/3) = 9Solve for x: Substitute the value back into the equation and solve for x. x^2 + x - 11 = 9 x^2 + x - 11 - 9 = 0 x^2 + x - 20 = 0Factor quadratic equation: Factor the quadratic equation. (x + 5)(x - 4) = 0Find values of x: Solve for the values of x. x + 5 = 0 or x - 4 = 0 x = -5 or x = 4

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Solve the equation: $2(x^{2}+x-11)^{\frac{3}{2}}=54$

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Grade 8

Solve multi-step equations with fractional coefficients

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Q. Solve the equation:

2(x^{2}+x-11)^{\frac{3}{2}}=54

Isolate term with exponent: Divide both sides of the equation by $2$ to isolate the term with the exponent. $\newline$ $2(x^2 + x - 11)^{\frac{3}{2}} = 54$ $\newline$ $(x^2 + x - 11)^{\frac{3}{2}} = \frac{54}{2}$ $\newline$ $(x^2 + x - 11)^{\frac{3}{2}} = 27$
Remove exponent: Take the reciprocal of the exponent $2/3$ to both sides to remove the exponent on the left side. $(x^2 + x - 11)^{(3/2)}]^{(2/3)} = 27^{(2/3)}$ $x^2 + x - 11 = 27^{(2/3)}$
Calculate value: Calculate the value of $27^{\frac{2}{3}}$ . $\newline$ $27^{\frac{2}{3}} = (3^3)^{\frac{2}{3}}$ $\newline$ $27^{\frac{2}{3}} = 3^{3*\frac{2}{3}}$ $\newline$ $27^{\frac{2}{3}} = 3^2$ $\newline$ $27^{\frac{2}{3}} = 9$
Solve for x: Substitute the value back into the equation and solve for x. $\newline$ $x^2 + x - 11 = 9$ $\newline$ $x^2 + x - 11 - 9 = 0$ $\newline$ $x^2 + x - 20 = 0$
Factor quadratic equation: Factor the quadratic equation. (x + \(5)(x - $4$ ) = $0$ \
Find values of x: Solve for the values of x. $\newline$ $x + 5 = 0$ or $x - 4 = 0$ $\newline$ $x = -5$ or $x = 4$