Solve Using the Quadratic Formula 1/16x^2-1/8x=1

Problem

1/16*x2−1/8*x=1

Solution

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

1/16*x2−1/8*x−1=0

2. Clear the fractions by multiplying the entire equation by the least common denominator, which is 16

x2−2*x−16=0

3. Identify the coefficients a b and c for use in the quadratic formula.

a=1

b=−2

c=−16

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

x=(−(−2)±√(,(−2)2−4*(1)*(−16)))/(2*(1))

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

x=(2±√(,4+64))/2

x=(2±√(,68))/2

6. Simplify the radical √(,68) by factoring out the largest perfect square, which is 4

√(,68)=√(,4⋅17)=2√(,17)

7. Substitute the simplified radical back into the expression and divide each term by 2

x=(2±2√(,17))/2

x=1±√(,17)

Final Answer

1/16*x2−1/8*x=1⇒x=1±√(,17)

Want more problems? Check here!