Solve Using the Quadratic Formula x^2-6x=40

Problem

x2−6*x=40

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by subtracting 40 from both sides.

x2−6*x−40=0

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

a=1

b=−6

c=−40

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

x=(−(−6)±√(,(−6)2−4*(1)*(−40)))/(2*(1))

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

x=(6±√(,36+160))/2

x=(6±√(,196))/2

5. Evaluate the square root of 196

x=(6±14)/2

6. Solve for both possible values of x by splitting the plus and minus signs.

x=(6+14)/2=20/2=10

x=(6−14)/2=(−8)/2=−4

Final Answer

x=10,−4

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