1. **State the problem:** Solve the quadratic equation $$5x^2 = 3 - x$$ and find the values of $x$ correct to 2 decimal places. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$5x^2 + x - 3 = 0$$ 3. **Identify coefficients:** The quadratic equation is in the form $$ax^2 + bx + c = 0$$ where: - $a = 5$ - $b = 1$ - $c = -3$ 4. **Use the quadratic formula:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 5. **Calculate the discriminant:** $$b^2 - 4ac = 1^2 - 4 \times 5 \times (-3) = 1 + 60 = 61$$ 6. **Calculate the square root of the discriminant:** $$\sqrt{61} \approx 7.81$$ 7. **Substitute values into the quadratic formula:** $$x = \frac{-1 \pm 7.81}{2 \times 5} = \frac{-1 \pm 7.81}{10}$$ 8. **Calculate the two solutions:** - For the plus sign: $$x = \frac{-1 + 7.81}{10} = \frac{6.81}{10} = 0.68$$ - For the minus sign: $$x = \frac{-1 - 7.81}{10} = \frac{-8.81}{10} = -0.88$$ 9. **Final answer:** $$x = 0.68 \text{ or } -0.88$$ These are the solutions to the equation correct to 2 decimal places.