Solve Using the Quadratic Formula x^2-4x+40=0

Problem

x2−4*x+40=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in standard form a*x2+b*x+c=0

a=1

b=−4

c=40

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

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

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

x=(4±√(,16−160))/2

x=(4±√(,−144))/2

5. Apply the imaginary unit i=√(,−1) to handle the square root of the negative number.

x=(4±12*i)/2

6. Divide each term in the numerator by the denominator to find the final solutions.

x=2±6*i

Final Answer

x=2±6*i

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