Solve Using the Quadratic Formula x^2-45=0

Problem

x2−45=0

Solution

1. Identify the coefficients for the quadratic equation in the form a*x2+b*x+c=0

a=1

b=0

c=−45

2. Apply the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a) by substituting the identified values.

x=(−0±√(,0−4*(1)*(−45)))/(2*(1))

3. Simplify the expression inside the square root (the discriminant).

x=(±√(,180))/2

4. Simplify the radical by factoring out the largest perfect square from 180 which is 36

√(,180)=√(,36⋅5)

√(,180)=6√(,5)

5. Divide the simplified radical by the denominator to find the final values of x

x=(±6√(,5))/2

x=±3√(,5)

Final Answer

x=±3√(,5)

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