Solve Using the Quadratic Formula x^2-4x+9=0

Problem

x2−4*x+9=0

Solution

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

a=1

b=−4

c=9

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)*(9)))/(2*(1))

4. Simplify the expression inside the square root, which is the discriminant.

x=(4±√(,16−36))/2

x=(4±√(,−20))/2

5. Simplify the square root of the negative number using the imaginary unit i where √(,−1)=i

√(,−20)=√(,4⋅5⋅−1)

√(,−20)=2*i√(,5)

6. Substitute the simplified radical back into the expression for x

x=(4±2*i√(,5))/2

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

x=2±i√(,5)

Final Answer

x=2±i√(,5)

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