Solve Using the Quadratic Formula x^2-75=0

Problem

x2−75=0

Solution

1. Identify the coefficients for the quadratic equation in the form a*x2+b*x+c=0 Here, a=1 b=0 and c=−75

2. Substitute these values into the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a)

3. Simplify the expression under the square root, known as the discriminant.

x=(−0±√(,0−4*(1)*(−75)))/(2*(1))

x=(±√(,300))/2

4. Simplify the radical by factoring out the largest perfect square. Since 300=100×3 we have √(,300)=10√(,3)

x=(±10√(,3))/2

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

x=±5√(,3)

Final Answer

x=±5√(,3)

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