Solve Using the Quadratic Formula x^2-6x=7/2

Problem

x^2−6*x=7/2

Solution

1. Rearrange the equation into standard form a*x^2+b*x+c=0 by subtracting 7/2 from both sides.

x^2−6*x−7/2=0

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

a=1

b=−6

c=−7/2

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

x=(−(−6)±√(,(−6)^2−4*(1)*(−7/2)))/(2*(1))

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

x=(6±√(,36+14))/2

x=(6±√(,50))/2

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

x=(6±5√(,2))/2

6. Split the expression into two separate solutions.

x=3±(5√(,2))/2

Final Answer

x=3+(5√(,2))/2,3−(5√(,2))/2

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