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

x=(−4±√(,4−4*(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.

x=(−4±12)/2

6. Solve for both possible values of x

x=(−4+12)/2=8/2=4

x=(−4−12)/2=(−16)/2=−8

Final Answer

x=4,−8

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