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

Problem

4*x2−5*x−7=0

Solution

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

a=4

b=−5

c=−7

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)2−4*(4)*(−7)))/(2*(4))

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

x=(5±√(,25+112))/8

x=(5±√(,137))/8

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

x=(5+√(,137))/8

x=(5−√(,137))/8

Final Answer

x=(5±√(,137))/8

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