(36-x)^2+(6+x)^2=900
Expanding the left side:
(36-x)^2 = (36-x)(36-x) = 1296 - 36x - 36x + x^2 = 1296 - 72x + x^2
(6+x)^2 = (6+x)(6+x) = 36 + 6x + 6x + x^2 = 36 + 12x + x^2
Now the equation becomes:
1296 - 72x + x^2 + 36 + 12x + x^2 = 900
Rearranging and combining like terms:
2x^2 - 60x + 432 = 0
Divide all terms by 2:
x^2 - 30x + 216 = 0
Now we need to factor this quadratic equation:
(x - 18)(x - 12) = 0
Setting each factor to zero:
x - 18 = 0 or x - 12 = 0
x = 18 or x = 12
Therefore, the solutions to the equation are x = 18 or x = 12.
(36-x)^2+(6+x)^2=900
Expanding the left side:
(36-x)^2 = (36-x)(36-x) = 1296 - 36x - 36x + x^2 = 1296 - 72x + x^2
(6+x)^2 = (6+x)(6+x) = 36 + 6x + 6x + x^2 = 36 + 12x + x^2
Now the equation becomes:
1296 - 72x + x^2 + 36 + 12x + x^2 = 900
Rearranging and combining like terms:
2x^2 - 60x + 432 = 0
Divide all terms by 2:
x^2 - 30x + 216 = 0
Now we need to factor this quadratic equation:
(x - 18)(x - 12) = 0
Setting each factor to zero:
x - 18 = 0 or x - 12 = 0
x = 18 or x = 12
Therefore, the solutions to the equation are x = 18 or x = 12.