Solve Using the Quadratic Formula x^2+3x-5=0

Problem

x2+3*x−5=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=3

c=−5

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=(−(3)±√(,(3)2−4*(1)*(−5)))/(2*(1))

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

x=(−3±√(,9+20))/2

x=(−3±√(,29))/2

5. Separate the expression into the two possible solutions for x

x=(−3+√(,29))/2

x=(−3−√(,29))/2

Final Answer

x=(−3±√(,29))/2

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