Solve Using the Quadratic Formula x^2-x=12

Problem

x2−x=12

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by subtracting 12 from both sides.

x2−x−12=0

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

a=1

b=−1

c=−12

3. Substitute these values into the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−1)±√(,(−1)2−4*(1)*(−12)))/(2*(1))

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

x=(1±√(,1+48))/2

x=(1±√(,49))/2

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

x=(1±7)/2

x=(1+7)/2⇒x=4

x=(1−7)/2⇒x=−3

Final Answer

x=4,−3

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