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