Question

Using factoring, which values are the solutions to the quadratic equation 2m2+7m−30=0?

A: m = - 10 or m = 3^2
B: m = -6 or m = 5^2
C: m = -5 or m = 3
D: m = 6 or m = -5^2

Answer 1

`\sf B. \quad m=-6 \quad or \quad m=(5)/(2)`

Step-by-step explanation:

Given equation:

`\sf 2m^2+7m-30=0`

Factor:

`\implies \sf 2m^2+12m-5m-30=0`

`\implies \sf 2m(m+6)-5(m+6)=0`

`\implies \sf (2m-5)(m+6)=0`

Therefore:

`\implies \sf 2m-5=0 \implies m=(5)/(2)`

`\implies \sf m+6=0 \implies m=-6`

Therefore, the solutions are:

`\sf m=-6 \quad or \quad m=(5)/(2)`

Answer 2

B: m = -6 or m = 5/2

Step-by-step explanation:

`\rightarrow \sf 2m^2 +7m - 30 = 0`

breakdown

`\rightarrow \sf 2m^2 +12m -5m- 30 = 0`

take out common factor

`\rightarrow \sf 2m(m +6) -5(m+ 6) = 0`

collect into groups

`\rightarrow \sf (2m -5)(m+ 6) = 0`

set to zero

`\rightarrow \sf 2m -5=0, \ m+ 6 = 0`

change sides

`\rightarrow \sf m=2.5, \ m= -6`