Solve Using the Quadratic Formula x^2-x-56=0

Problem

x2−x−56=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=−1

c=−56

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*(1)*(−56)))/(2*(1))

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

x=(1±√(,1+224))/2

x=(1±√(,225))/2

5. Evaluate the square root of 225

x=(1±15)/2

6. Solve for the two possible values of x by calculating the plus and minus cases.

x=(1+15)/2=16/2=8

x=(1−15)/2=(−14)/2=−7

Final Answer

x=8,−7

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