Solve Using the Quadratic Formula x^2+10x+24=0

Problem

x2+10*x+24=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=10

c=24

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=(−10±√(,10−4*(1)*(24)))/(2*(1))

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

x=(−10±√(,100−96))/2

x=(−10±√(,4))/2

5. Evaluate the square root and simplify the fraction.

x=(−10±2)/2

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

x=(−10+2)/2=(−8)/2=−4

x=(−10−2)/2=(−12)/2=−6

Final Answer

x=−4,−6

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