Question

solve the equation for c.
$c^2 = -12c$
show your work here
$c = $
$c = $

Explanation:

Step1: Move all terms to left

To solve the quadratic equation \( c^{2} = -12c \), we first move all terms to one side of the equation. Add \( 12c \) to both sides:
\( c^{2}+ 12c=0 \)

Step2: Factor the left side

Factor out the common factor \( c \) from the left - hand side of the equation:
\( c(c + 12)=0 \)

Step3: Apply the zero - product property

According to the zero - product property, if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \). So we set each factor equal to zero and solve for \( c \):

• Case 1: If \( c=0 \), then the equation is satisfied.
• Case 2: If \( c + 12=0 \), we solve for \( c \) by subtracting 12 from both sides: \( c=- 12 \)

Answer:

\( c = 0 \)
\( c=-12 \)