Solve the following quadratic equation for all values of xx in simplest form.3, left bracket, 3, x, plus, 1, right bracket, squared, minus, 43, equals, minus, 133(3x+1) 2 −43=−13
Question
Solve the following quadratic equation for all values of xx in simplest form.3, left bracket, 3, x, plus, 1, right bracket, squared, minus, 43, equals, minus, 133(3x+1) 2 −43=−13
Solution
The equation you've provided seems to have a typo. It should probably be either "(3x+1)^2 - 43 = -13" or "3(3x+1)^2 - 43 = -13".
Let's solve the first one:
- Simplify the equation: (3x+1)^2 - 43 = -13
- Add 43 to both sides to isolate the square on one side: (3x+1)^2 = 30
- Take the square root of both sides: 3x + 1 = ±√30
- Subtract 1 from both sides: 3x = -1 ±√30
- Divide by 3 to solve for x: x = (-1 ±√30) / 3
So the solutions are x = (-1 + √30) / 3 and x = (-1 - √30) / 3.
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