Question

Solve the quadratic equation (6u + 1)² = 25 using the square roots property.

a) u = -1/2
b) u = -3/2
c) u = 1/2
d) u = 3/2

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf (6u + 1)^2 = 25$}`

`\Large \text{$ \sf 6u + 1 = \pm√(25)$}`

`\Large \text{$ \sf 6u + 1 = 5$}`

`\Large \text{$ \sf 6u = 5 - 1$}`

`\Large \text{$ \sf 6u = 4$}`

`\Large \text{$ \sf u = (4)/(6) = (2)/(3)$}`

`\Large \text{$ \sf 6u + 1 = -5$}`

`\Large \text{$ \sf 6u = -5 - 1$}`

`\Large \text{$ \sf 6u = -6$}`

`\Large \text{$ \sf u = -(6)/(6)$}`

`\Large \text{$ \sf u = -1$}`

`\Large \text{$ \sf S = \left\{(2)/(3),\:-1\right\}$}`

Answer 2

To solve the quadratic equation (6u + 1)² = 25, you need to expand the equation, subtract 25 from both sides, and then apply the quadratic formula to find the solutions. The solutions to the equation are u = 2/3 and u = -1.

Step-by-step explanation:

To solve the quadratic equation (6u + 1)² = 25 using the square roots property:

1. Expand the equation: (6u + 1)² = 25 becomes 36u² + 12u + 1 = 25.
2. Subtract 25 from both sides of the equation to get 36u² + 12u - 24 = 0.
3. Apply the quadratic formula: u = (-b ± √(b² - 4ac)) / (2a), where a = 36, b = 12, and c = -24.
4. Solve the equation using the quadratic formula: u = (-12 ± √(12² - 4*36*(-24))) / (2*36).
5. Simplify the equation: u = (-12 ± √(144 + 3456)) / 72.
6. Compute the square root: u = (-12 ± √(3600)) / 72.
7. Further simplify: u = (-12 ± 60) / 72.
8. Calculate both solutions: u = (-12 + 60) / 72 = 48 / 72 = 2/3 and u = (-12 - 60) / 72 = -72 / 72 = -1.

Therefore, the solutions to the quadratic equation (6u + 1)² = 25 are u = 2/3 and u = -1.