Solve Using the Quadratic Formula 1/4x^2-1/2x=1

Problem

1/4*x2−1/2*x=1

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by subtracting 1 from both sides.

1/4*x2−1/2*x−1=0

2. Identify the coefficients a b and c for the quadratic formula.

a=1/4

b=−1/2

c=−1

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

x=(−(−1/2)±√(,(−1/2)2−4*(1/4)*(−1)))/(2*(1/4))

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

x=(1/2±√(,1/4+1))/1/2

5. Combine the terms under the radical.

x=(1/2±√(,5/4))/1/2

6. Evaluate the square root of the fraction.

x=(1/2±√(,5)/2)/1/2

7. Divide each term in the numerator by the denominator to find the final values of x

x=1±√(,5)

Final Answer

1/4*x2−1/2*x=1⇒x=1±√(,5)

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