Solve Using the Quadratic Formula x^2-10x+16=0

Problem

x2−10*x+16=0

Solution

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

a=1

b=−10

c=16

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=(−(−10)±√(,(−10)2−4*(1)*(16)))/(2*(1))

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

x=(10±√(,100−64))/2

x=(10±√(,36))/2

5. Evaluate the square root and simplify the fraction.

x=(10±6)/2

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

x=(10+6)/2=16/2=8

x=(10−6)/2=4/2=2

Final Answer

x=8,2

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