Solve Using the Quadratic Formula x^2-27=0

Problem

x2−27=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 Here, a=1 b=0 and c=−27

2. Apply the formula for the quadratic equation, which is x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values into the formula:

x=(−0±√(,0−4*(1)*(−27)))/(2*(1))

4. Simplify the expression inside the square root:

x=(±√(,108))/2

5. Simplify the radical by factoring out the largest perfect square from 108 which is 36

x=(±√(,36⋅3))/2

x=(±6√(,3))/2

6. Divide by the denominator to find the final values for x

x=±3√(,3)

Final Answer

x=±3√(,3)

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