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Answer

Step‑by‑step solution

1. Write the equation in standard form
   The given quadratic is already in standard form

   $$2x^{2} - 8x + 6 = 0$$

2. Identify the coefficients
   Compare with $ax^{2}+bx+c=0$:

   • $a = 2$
   • $b = -8$
   • $c = 6$

3. Apply the quadratic formula

   $$x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$$

4. Plug in the coefficients

   $$x = \frac{-(-8) \pm \sqrt{(-8)^{2} - 4(2)(6)}}{2(2)}$$

5. Simplify inside the square root

   $$(-8)^{2} = 64 \\ 4ac = 4 \times 2 \times 6 = 48 \\ b^{2} - 4ac = 64 - 48 = 16$$

6. Continue simplifying

   $$x = \frac{8 \pm \sqrt{16}}{4}$$

   Since $\sqrt{16}=4$,

   $$x = \frac{8 \pm 4}{4}$$

7. Separate the two possible solutions

   • Using the “+” sign:

     $$x = \frac{8 + 4}{4} = \frac{12}{4} = 3$$

   • Using the “–” sign:

     $$x = \frac{8 - 4}{4} = \frac{4}{4} = 1$$

8. Write the final solution set

   $$x = 1 \;\; \text{or} \;\; x = 3$$

Want a visual walkthrough of the quadratic formula?

YouTube video suggestion: (automatically provided for conceptual help)

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