Solve Using the Quadratic Formula x^2+30x+200=0

Problem

x2+30*x+200=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=30

c=200

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=(−30±√(,30−4*(1)*(200)))/(2*(1))

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

x=(−30±√(,900−800))/2

x=(−30±√(,100))/2

5. Evaluate the square root and split the equation into two possible solutions for x

x=(−30±10)/2

6. Calculate the first solution using the plus sign.

(x_1)=(−30+10)/2

(x_1)=(−20)/2

(x_1)=−10

7. Calculate the second solution using the minus sign.

(x_2)=(−30−10)/2

(x_2)=(−40)/2

(x_2)=−20

Final Answer

x=−10,−20

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