Quadratic Coefficients B5948B

1. **State the problem:** We are given the equation $3^2 + 8 = 3$ and asked to identify coefficients $a$, $b$, and $c$ for the quadratic formula, then solve for $x$. 2. **Analyze the equation:** The equation $3^2 + 8 = 3$ simplifies to $9 + 8 = 3$, which is $17 = 3$, a false statement. This means the equation as given is not a quadratic equation in $x$. 3. **Assumption:** Likely, the original equation was misstated. A quadratic equation generally has the form $$ax^2 + bx + c = 0$$. 4. **Hypothesis:** If the intended equation was $3x^2 + 8 = 3$, then we can rewrite it as: $$3x^2 + 8 = 3$$ Subtract 3 from both sides: $$3x^2 + 8 - 3 = 0$$ $$3x^2 + 5 = 0$$ 5. **Identify coefficients:** Comparing to $ax^2 + bx + c = 0$: - $a = 3$ - $b = 0$ (no $x$ term) - $c = 5$ 6. **Use quadratic formula:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Substitute values: $$x = \frac{-0 \pm \sqrt{0^2 - 4 \times 3 \times 5}}{2 \times 3} = \frac{\pm \sqrt{-60}}{6}$$ 7. **Simplify the discriminant:** $$\sqrt{-60} = \sqrt{-1 \times 4 \times 15} = 2i\sqrt{15}$$ 8. **Final solutions:** $$x = \frac{\pm 2i\sqrt{15}}{6} = \pm \frac{i\sqrt{15}}{3}$$ 9. **Answer:** - $a = 3$ - $b = 0$ - $c = 5$ - $x_1 = -\frac{i\sqrt{15}}{3}$ - $x_2 = \frac{i\sqrt{15}}{3}$ Since the problem asks for integer answers for $x$, and the solutions are complex, there are no integer solutions for $x$. **Summary:** The coefficients are $a=3$, $b=0$, $c=5$. The solutions for $x$ are complex and not integers. **Note:** If the original equation is different, please clarify.