Solve Using the Quadratic Formula x^2+10x=-21

Problem

x2+10*x=−21

Solution

1. Rewrite the equation in standard form a*x2+b*x+c=0 by adding 21 to both sides.

x2+10*x+21=0

2. Identify the coefficients a b and c for the quadratic formula.

a=1

b=10

c=21

3. Apply the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a) by substituting the identified values.

x=(−10±√(,10−4*(1)*(21)))/(2*(1))

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

x=(−10±√(,100−84))/2

x=(−10±√(,16))/2

5. Evaluate the square root.

x=(−10±4)/2

6. Solve for both possible values of x

x=(−10+4)/2⇒x=−3

x=(−10−4)/2⇒x=−7

Final Answer

x=−3,−7

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