To solve the quadratic equation $5(x + 5)^2 - 38 = -18$, follow these steps:

1. Rewrite the equation by moving $-18$ to the other side:

   $5(x + 5)^2 - 38 + 18 = 0$

   Simplify the constants on the left side:

   $5(x + 5)^2 - 20 = 0$

2. Isolate the term containing $(x + 5)^2$ by moving $-20$ to the other side:

   $5(x + 5)^2 = 20$

3. Divide both sides by 5 to simplify:

   $(x + 5)^2 = 4$

4. Take the square root of both sides to solve for $x + 5$:

   $x + 5 = \pm 2$

5. Solve for $x$ by isolating it in each case:

   • If $x + 5 = 2$:

     $x = 2 - 5 = -3$

   • If $x + 5 = -2$:

     $x = -2 - 5 = -7$

6. List the solutions:

   $x = -3 \quad \text{and} \quad x = -7$

So, the solutions to the equation are:

$x = -3 \text{ and } x = -7$

Would you like a more detailed explanation of any step, or do you have additional questions?

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Related Questions

1. How do you solve quadratic equations when they don’t factor easily?
2. Can you explain the process of completing the square for quadratic equations?
3. How do you solve quadratic equations using the quadratic formula?
4. What is the significance of $\pm$ in square root operations when solving equations?
5. How would you solve a quadratic equation with complex roots?

Tip:

When taking the square root of both sides in an equation, remember to consider both the positive and negative square roots to find all possible solutions.