Solve Using the Quadratic Formula 4x^2-7x-5=0

Problem

4*x2−7*x−5=0

Solution

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

a=4

b=−7

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 identified values into the quadratic formula.

x=(−(−7)±√(,(−7)2−4*(4)*(−5)))/(2*(4))

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

x=(7±√(,49+80))/8

x=(7±√(,129))/8

5. Determine the two possible values for x based on the plus-minus sign.

x=(7+√(,129))/8

x=(7−√(,129))/8

Final Answer

x=(7±√(,129))/8

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