Let's first expand both sides of the equation to simplify it:
Expanding the left side:(3x + 15)^2 = (3x + 15)(3x + 15)= 9x^2 + 45x + 45x + 225= 9x^2 + 90x + 225
Expanding the right side:(3x - 9)^2 = (3x - 9)(3x - 9)= 9x^2 - 27x - 27x + 81= 9x^2 - 54x + 81
Now we have:9x^2 + 90x + 225 = 9x^2 - 54x + 81
Subtracting 9x^2 from both sides:90x + 225 = -54x + 81144x + 225 = 81144x = -144x = -1
So, the solution for the first equation is x = -1.
Now let's solve the second equation:
(x - 5)(x - 3) + 1 = 0Expanding:x^2 - 3x - 5x + 15 + 1 = 0x^2 - 8x + 16 = 0(x - 4)(x - 4) = 0(x - 4)^2 = 0x - 4 = 0x = 4
Therefore, the solutions for the second equation are x = 4.
In conclusion, the solutions to the system of equations are x = -1 and x = 4.
Let's first expand both sides of the equation to simplify it:
Expanding the left side:
(3x + 15)^2 = (3x + 15)(3x + 15)
= 9x^2 + 45x + 45x + 225
= 9x^2 + 90x + 225
Expanding the right side:
(3x - 9)^2 = (3x - 9)(3x - 9)
= 9x^2 - 27x - 27x + 81
= 9x^2 - 54x + 81
Now we have:
9x^2 + 90x + 225 = 9x^2 - 54x + 81
Subtracting 9x^2 from both sides:
90x + 225 = -54x + 81
144x + 225 = 81
144x = -144
x = -1
So, the solution for the first equation is x = -1.
Now let's solve the second equation:
(x - 5)(x - 3) + 1 = 0
Expanding:
x^2 - 3x - 5x + 15 + 1 = 0
x^2 - 8x + 16 = 0
(x - 4)(x - 4) = 0
(x - 4)^2 = 0
x - 4 = 0
x = 4
Therefore, the solutions for the second equation are x = 4.
In conclusion, the solutions to the system of equations are x = -1 and x = 4.