Solve Using the Quadratic Formula x^2-4x-7=0

Problem

x2−4*x−7=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=−7

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

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the identified values into the quadratic formula.

x=(−(−4)±√(,(−4)2−4*(1)*(−7)))/(2*(1))

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

x=(4±√(,16+28))/2

x=(4±√(,44))/2

5. Simplify the radical by factoring out the largest perfect square.

x=(4±√(,4⋅11))/2

x=(4±2√(,11))/2

6. Divide each term in the numerator by the denominator to find the final values of x

x=2±√(,11)

Final Answer

x=2±√(,11)

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