Solve Using the Quadratic Formula 5x^2+5x-1=0

Problem

5*x2+5*x−1=0

Solution

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

a=5

b=5

c=−1

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=(−5±√(,5−4*(5)*(−1)))/(2*(5))

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

x=(−5±√(,25+20))/10

x=(−5±√(,45))/10

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

√(,45)=√(,9⋅5)=3√(,5)

x=(−5±3√(,5))/10

Final Answer

x=(−5±3√(,5))/10

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