Solve Using the Quadratic Formula 4x^2-4x=11

Problem

4*x2−4*x=11

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by subtracting 11 from both sides.

4*x2−4*x−11=0

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

a=4

b=−4

c=−11

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

x=(−(−4)±√(,(−4)2−4*(4)*(−11)))/(2*(4))

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

x=(4±√(,16+176))/8

x=(4±√(,192))/8

5. Simplify the radical by factoring out the largest perfect square from 192 which is 64

√(,192)=√(,64⋅3)=8√(,3)

x=(4±8√(,3))/8

6. Divide both terms in the numerator by the denominator to find the final simplified values for x

x=4/8±(8√(,3))/8

x=1/2±√(,3)

Final Answer

x=(1±2√(,3))/2

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