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

19, plus, 2, x, squared, equals, 21

19+2*x*2=

21

To solve the equation \( 19 + 2x^2 = 21 \), follow these steps:

1. **Subtract 19 from both sides**:
   \[
   2x^2 = 21 - 19
   \]
   \[
   2x^2 = 2
   \]

2. **Divide both sides by 2**:
   \[
   x^2 = \frac{2}{2}
   \]
   \[
   x^2 = 1
   \]

3. **Take the square root of both sides**:
   \[
   x = \pm 1
   \]

Thus, the solutions are:
\[
x = 1 \quad \text{and} \quad x = -1
\]

### Summary of Solutions:
- \( x = 1 \)
- \( x = -1 \)

Would you like any details on the steps? Here are some related questions for further exploration:

1. How can you verify these solutions by substituting them back into the original equation?
2. What would happen if the equation were \( 19 + 2x^2 = 25 \)?
3. Can you explain the significance of the discriminant in quadratic equations?
4. What are some graphical representations of this equation?
5. How do you solve a quadratic equation using the quadratic formula?

**Tip**: Always check your solutions by plugging them back into the original equation to ensure they satisfy it.

Solve the following quadratic equation for all values of x*x in simplest form: 19 + 2*x^2 = 21.

Explore how to solve the quadratic equation 19 + 2x^2 = 21 with a comprehensive step-by-step solution. This problem highlights essential algebraic concepts, including solving for x using the quadratic formula and the square root principle. Ideal for students in Grades 7-9.

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