Find all real solutions of the equation 2(a+6)2−14=574 After simplifying, the solutions to this equation look like a=A±B√C

Question

Find all real solutions of the equation 2(a+6)2−14=574 After simplifying, the solutions to this equation look like a=A±B√C

Answer 1

To solve this equation you need to get a to one side of the equation by itself.

Start of by adding 14 to each side.

2(a+6)²-14+14=574+14

Simplify

2(a+6)²=588

Divide both sides by 2

2(a+6)²/2=588/2

Simplify

(a+6)²=294

Take the square root of both sides√

√(a+6)²=√294

Simplify (To simplify the radical, use the prime factors of 294=2x3x7x7)

a+6=±7√6

Subtract 6 from both sides

a+6-6=-6±7√6

Simplify

a=-6±7√6 is the final answer