Solve for p 2p^2=-4p+1

Problem

2*p2=−4*p+1

Solution

1. Rearrange the equation into standard quadratic form a*x2+b*x+c=0 by adding 4*p and subtracting 1 from both sides.

2*p2+4*p−1=0

2. Identify the coefficients for the quadratic formula p=(−b±√(,b2−4*a*c))/(2*a)

a=2

b=4

c=−1

3. Substitute the coefficients into the quadratic formula.

p=(−4±√(,4−4*(2)*(−1)))/(2*(2))

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

p=(−4±√(,16+8))/4

p=(−4±√(,24))/4

5. Simplify the radical by factoring out the largest perfect square.

p=(−4±2√(,6))/4

6. Divide the numerator and denominator by their greatest common factor, which is 2

p=(−2±√(,6))/2

Final Answer

p=(−2±√(,6))/2

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