First we need to expand both sides of the equation:
(3x-1)^2 = (3x-1)(3x-1) = 9x^2 - 6x + 1
(4x+5)^2 = (4x+5)(4x+5) = 16x^2 + 40x + 25
(5x-7)^2 = (5x-7)(5x-7) = 25x^2 - 70x + 49
Now we can substitute these back into the equation:
(9x^2 - 6x + 1) + (16x^2 + 40x + 25) = 25x^2 - 70x + 49
Simplify the equation:
25x^2 - 6x + 1 + 16x^2 + 40x + 25 = 25x^2 - 70x + 49
41x^2 + 34x + 26 = 25x^2 - 70x + 49
Now, let's simplify further by combining like terms:
41x^2 + 34x + 26 - 25x^2 + 70x -49 = 0
16x^2 + 104x - 23 = 0
Since this is a quadratic equation, we can try to solve it by factoring, completing the square, or using the quadratic formula.
First we need to expand both sides of the equation:
(3x-1)^2 = (3x-1)(3x-1) = 9x^2 - 6x + 1
(4x+5)^2 = (4x+5)(4x+5) = 16x^2 + 40x + 25
(5x-7)^2 = (5x-7)(5x-7) = 25x^2 - 70x + 49
Now we can substitute these back into the equation:
(9x^2 - 6x + 1) + (16x^2 + 40x + 25) = 25x^2 - 70x + 49
Simplify the equation:
25x^2 - 6x + 1 + 16x^2 + 40x + 25 = 25x^2 - 70x + 49
41x^2 + 34x + 26 = 25x^2 - 70x + 49
Now, let's simplify further by combining like terms:
41x^2 + 34x + 26 - 25x^2 + 70x -49 = 0
16x^2 + 104x - 23 = 0
Since this is a quadratic equation, we can try to solve it by factoring, completing the square, or using the quadratic formula.