Solve the equation 6(2x + 4)² = (2x + 4) + 2.

Solution:

Given equation is

6(2x + 4)² = (2x + 4) + 2

We know that (a + b)² = a² + 2ab + b²

6{(2x)² + 2(2x)(4) + 16} = 2x + 4 + 2

6{4x² + 16x + 16} = 2x + 6

24x² + 96x + 96 = 2x + 6

24x² + 96x + 96 - 2x - 6 = 0

24x² + 94x + 90 = 0

12x² + 47x + 45 = 0

x = -b ± √(b² - 4ac) / 2a

x = -47 ± √(47² - 4(12)(45)) / 2(12)

x = -47 ± √2209 - 2160 /24

x = -47 ± √49 /24

x = -47 ± 7 /24

x = -2.25, -1.66

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Solve the equation 6(2x + 4)² = (2x + 4) + 2.

Summary:

By solving 6(2x + 4)² = (2x + 4) + 2, we get x = -2.25 and -1.66.