What is the answer to (x^2-x-22)^{3/2}=27 ?

The answer to (x^2-x-22)^{3/2}=27 is x=(1+5*5^{1/2})/2 ,x=(1-5*5^{1/2})/2

Solve for x: (x^2-x-22)^{3/2}=27

The solution is x=(1+5*5^{1/2})/2 ,x=(1-5*5^{1/2})/2

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(x^{2} - x - 22)^{\frac{3}{2}} = 27

x = \frac{1 + 5 \cdot 5 ^{\frac{1}{2}}}{2}, x = \frac{1 - 5 \cdot 5 ^{\frac{1}{2}}}{2}

Decimal

x = 6.09016 \dots, x = - 5.09016 \dots

Solution steps

(x^{2} - x - 22)^{\frac{3}{2}} = 27

Take both sides of the equation to the power of

2 : (x^{2} - x - 22)^{3} = 729

(x^{2} - x - 22)^{3} = 729

Solve

(x^{2} - x - 22)^{3} = 729 : x = \frac{1 + 5 \cdot 5 ^{\frac{1}{2}}}{2}, x = \frac{1 - 5 \cdot 5 ^{\frac{1}{2}}}{2}

x = \frac{1 + 5 \cdot 5 ^{\frac{1}{2}}}{2}, x = \frac{1 - 5 \cdot 5 ^{\frac{1}{2}}}{2}

Verify Solutions:

x = \frac{1 + 5 \cdot 5 ^{\frac{1}{2}}}{2}

True

, x = \frac{1 - 5 \cdot 5 ^{\frac{1}{2}}}{2}

True

The solutions are

x = \frac{1 + 5 \cdot 5 ^{\frac{1}{2}}}{2}, x = \frac{1 - 5 \cdot 5 ^{\frac{1}{2}}}{2}

5 - 3 x + 1 = 0

3 x = - 2

3 x + 12 = 9

x + 13 - 7 - x = 2

2 x + 2 - x + 2 = 1

What is the answer to (x^2-x-22)^{3/2}=27 ?
The answer to (x^2-x-22)^{3/2}=27 is x=(1+5*5^{1/2})/2 ,x=(1-5*5^{1/2})/2
Solve for x: (x^2-x-22)^{3/2}=27
The solution is x=(1+5*5^{1/2})/2 ,x=(1-5*5^{1/2})/2