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

Question

13, plus, 3, x, squared, equals, 16
13+3x
2
=
16

Answer 1

To solve the quadratic equation \( 13 + 3x^2 = 16 \), we first rearrange it into standard form.

1. Subtract 16 from both sides: \[ 13 + 3x^2 - 16 = 0 \] This simplifies to: \[ 3x^2 - 3 = 0 \]

2. Next, we can factor out a 3: \[ 3(x^2 - 1) = 0 \]

3. Now, setting the equation inside the parentheses to zero gives us: \[ x^2 - 1 = 0 \]

4. This can be factored further: \[ (x - 1)(x + 1) = 0 \]

5. Setting each factor to zero gives us the solutions: \[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \] \[ x + 1 = 0 \quad \Rightarrow \quad x = -1 \]

Thus, the solutions to the quadratic equation \( 13 + 3x^2 = 16 \) are: \[ \boxed{1} \quad \text{and} \quad \boxed{-1} \]