1. **Problem statement:** Solve the quadratic equation $x^2 + 6x + 5 = 0$ by completing the square. 2. **Step 1: Move constant to the other side.** $$x^2 + 6x = -5$$ 3. **Step 2: Complete the square.** Take half the coefficient of $x$, which is $6$, half is $3$, then square it, $3^2 = 9$. Add $9$ to both sides: $$x^2 + 6x + 9 = -5 + 9$$ $$ (x + 3)^2 = 4 $$ 4. **Step 3: Take square roots of both sides.** $$ x + 3 = \pm 2 $$ 5. **Step 4: Solve for $x$.** $$ x = -3 \pm 2 $$ 6. **Step 5: Find the two solutions.** $$ x_1 = -3 + 2 = -1 $$ $$ x_2 = -3 - 2 = -5 $$ **Final answer:** The solutions are $x = -1$ and $x = -5$. --- 1. **Problem statement:** Solve the quadratic equation $2x^2 + 8x - 10 = 0$ by completing the square. 2. **Step 1: Divide all terms by the coefficient of $x^2$ (which is 2).** $$ x^2 + 4x - 5 = 0 $$ 3. **Step 2: Move constant term to the other side.** $$ x^2 + 4x = 5 $$ 4. **Step 3: Complete the square.** Take half of $4$ is $2$, square it: $2^2 = 4$. Add $4$ to both sides: $$ x^2 + 4x + 4 = 5 + 4 $$ $$ (x + 2)^2 = 9 $$ 5. **Step 4: Take square roots.** $$ x + 2 = \pm 3 $$ 6. **Step 5: Solve for $x$.** $$ x = -2 \pm 3 $$ 7. **Step 6: Find the two solutions.** $$ x_1 = -2 + 3 = 1 $$ $$ x_2 = -2 - 3 = -5 $$ **Final answer:** The solutions are $x = 1$ and $x = -5$.