Solve Using the Quadratic Formula x^2-4x=32

Problem

x2−4*x=32

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by subtracting 32 from both sides.

x2−4*x−32=0

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

a=1

b=−4

c=−32

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

x=(−(−4)±√(,(−4)2−4*(1)*(−32)))/(2*(1))

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

x=(4±√(,16+128))/2

x=(4±√(,144))/2

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

x=(4±12)/2

(x_1)=(4+12)/2=16/2=8

(x_2)=(4−12)/2=(−8)/2=−4

Final Answer

x=8,−4

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