Let's solve the first equation:
(×-5)² = 3× + 25Expanding the left side:(x² - 10x + 25) = 3x + 25Now, bring all terms to one side:x² - 10x - 3x = 0x² - 13x = 0x(x - 13) = 0x = 0 or x = 13
Now let's solve the second equation:
(9-4x)² = 5(4x+1)Expanding the left side:(81 - 72x + 16x²) = 20x + 5Rearranging terms:16x² - 72x - 20x + 81 - 5 = 016x² - 92x + 76 = 0Divide by 4 to simplify:4x² - 23x + 19 = 0Using the quadratic formula:x = (23 ± √(529 - 304))/8x = (23 ± √225)/8x = (23 ± 15)/8x = 38/8 = 4.75 or x = 8/8 = 1
Thus, the solutions are x = 0, x = 13, x = 4.75, x = 1.
Let's solve the first equation:
(×-5)² = 3× + 25
Expanding the left side:
(x² - 10x + 25) = 3x + 25
Now, bring all terms to one side:
x² - 10x - 3x = 0
x² - 13x = 0
x(x - 13) = 0
x = 0 or x = 13
Now let's solve the second equation:
(9-4x)² = 5(4x+1)
Expanding the left side:
(81 - 72x + 16x²) = 20x + 5
Rearranging terms:
16x² - 72x - 20x + 81 - 5 = 0
16x² - 92x + 76 = 0
Divide by 4 to simplify:
4x² - 23x + 19 = 0
Using the quadratic formula:
x = (23 ± √(529 - 304))/8
x = (23 ± √225)/8
x = (23 ± 15)/8
x = 38/8 = 4.75 or x = 8/8 = 1
Thus, the solutions are x = 0, x = 13, x = 4.75, x = 1.