Question

Please help me solve for x in the following magic square...​

Answer 1

Answer:

x = 1/2

Step-by-step explanation:

The sum of numbers in all rows, columns and diagonals have to be the same.

Notice the diagonals do not have an x so let's sum those numbers to see what the sum for all must be.

-2+(1/2) +3 = (-4+1+6)/2 = 3/2

-5+(1/2)+6 = (-10+1+12)/2 = 3/2

Now we can pick the first row and sum the numbers up knowing that the result should be 3/2, will find x

-2+x-3+6 = 3/2, combine like terms

         x+1 = 3/2 , subtract 1 from both sides

            x = (3/2)-1, find common denominator and subtract

            x = (3-2)/2, combine like terms

            x = 1/2

Check or work:

Rows from top to down

-2 +(1/2) -3 +6 = (-4+1-6+12)/2 = 3/2✅

17*(1/2) +(1/2) +(1/2)-8 = (17+1+1-16)/2 = 3/2✅

-5+(9/2) -2(1/2) +3 = (-10+9-2+6)/2 = 3/2✅

Columns from left to right

-2+17(1/2)-5 = (-4+17-10)/2 =3/2✅

(1/2)-3+(1/2)+(9/2)-2(1/2) = (1-6+1+9-2)/2 = 3/2✅

6+(1/2)-8+3 = (12+1-16+6)/2 = 3/2✅

Diagonals

-2+(1/2) +3 = (-4+1+6)/2 = 3/2✅

-5+(1/2)+6 = (-10+1+12)/2 = 3/2✅