Solve Using the Quadratic Formula x^2-10x-4=0

Problem

x2−10*x−4=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=−10

c=−4

2. Apply the formula for the quadratic equation, which is x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−10)±√(,(−10)2−4*(1)*(−4)))/(2*(1))

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

x=(10±√(,100+16))/2

x=(10±√(,116))/2

4. Factor the square root by finding the largest perfect square divisor of 116

√(,116)=√(,4⋅29)=2√(,29)

5. Substitute the simplified radical back into the equation and divide each term by the denominator.

x=(10±2√(,29))/2

x=5±√(,29)

Final Answer

x=5±√(,29)

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