Solve the following quadratic equation for all values of xx in simplest form.

Question

3, left parenthesis, x, squared, plus, 1, right parenthesis, minus, 5, equals, 7
3(x
2
+1)−5=
7

Answer 1

To solve the quadratic equation \( 3(x^2 + 1) - 5 = 7 \), we will first simplify the equation step by step.

1. Start with the original equation: \[ 3(x^2 + 1) - 5 = 7 \]

2. Distribute the 3: \[ 3x^2 + 3 - 5 = 7 \]

3. Combine like terms: \[ 3x^2 - 2 = 7 \]

4. Add 2 to both sides of the equation: \[ 3x^2 = 9 \]

5. Divide both sides by 3: \[ x^2 = 3 \]

6. Take the square root of both sides: \[ x = \pm \sqrt{3} \]

So, the solutions to the equation are: \[ x = \sqrt{3} \quad \text{and} \quad x = -\sqrt{3} \]