Frankie performed the following steps to solve the equation 2m^2−24m=−54
.
Step 1: 2m^2−24m+54=0
Step 2: 2(m^2−12m+27)=0
Step 3: 2(m−9)(m−3)=0
Step 4: m=−9, −3, 2
Frankie's steps are incorrect.
The correct steps to solve the equation 2m^2−24m=−54 are:
Step 1: Add 54 to both sides of the equation to bring all terms to one side:
2m^2 - 24m + 54 = -54 + 54
2m^2 - 24m + 54 = 0
Step 2: Factor the quadratic expression
2(m^2 - 12m + 27) = 0
2(m - 9)(m - 3) = 0
Step 3: Set each factor equal to 0 and solve for m,
m - 9 = 0 or m - 3 = 0
m = 9 or m = 3
Therefore, the correct solution to the equation is m = 9 or m = 3.