Solve Using the Quadratic Formula 5x^2-x-4=0

Problem

5*x2−x−4=0

Solution

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

a=5

b=−1

c=−4

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=(−(−1)±√(,(−1)2−4*(5)*(−4)))/(2*(5))

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

x=(1±√(,1+80))/10

x=(1±√(,81))/10

5. Evaluate the square root.

x=(1±9)/10

6. Solve for the two possible values of x by calculating both the addition and subtraction cases.

x=(1+9)/10=10/10=1

x=(1−9)/10=(−8)/10=−4/5

Final Answer

x=1,−4/5

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