Solve Using the Quadratic Formula x^2-2x=24

Problem

x2−2*x=24

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by subtracting 24 from both sides.

x2−2*x−24=0

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

a=1

b=−2

c=−24

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

x=(−(−2)±√(,(−2)2−4*(1)*(−24)))/(2*(1))

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

x=(2±√(,4+96))/2

x=(2±√(,100))/2

5. Evaluate the square root and solve for both possible values of x

x=(2±10)/2

6. Calculate the first solution using the plus sign.

x=(2+10)/2=12/2=6

7. Calculate the second solution using the minus sign.

x=(2−10)/2=(−8)/2=−4

Final Answer

x=6,−4

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