Solve for x in the equation x squared + 2 x + 1 = 17.
x = negative 1 plus-or-minus StartRoot 15 EndRoot
x = negative 1 plus-or-minus StartRoot 17 EndRoot
x = negative 2 plus-or-minus 2 StartRoot 5 EndRoot

We are given the equation \( x^2 + 2x + 1 = 17 \). First, we will solve this equation step by step.

### Step 1: Simplify the equation
Rewrite the equation in standard quadratic form:

\[
x^2 + 2x + 1 = 17
\]

Subtract 17 from both sides to set the equation to 0:

\[
x^2 + 2x + 1 - 17 = 0
\]

\[
x^2 + 2x - 16 = 0
\]

Now, we have a quadratic equation:

\[
x^2 + 2x - 16 = 0
\]

### Step 2: Use the quadratic formula

The quadratic formula is:

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

For the equation \(x^2 + 2x - 16 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 2\)
- \(c = -16\)

Substitute these values into the quadratic formula:

\[
x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-16)}}{2(1)}
\]

Simplify inside the square root:

\[
x = \frac{-2 \pm \sqrt{4 + 64}}{2}
\]

\[
x = \frac{-2 \pm \sqrt{68}}{2}
\]

\[
x = \frac{-2 \pm \sqrt{4 \times 17}}{2}
\]

\[
x = \frac{-2 \pm 2\sqrt{17}}{2}
\]

### Step 3: Simplify the expression

\[
x = \frac{-2}{2} \pm \frac{2\sqrt{17}}{2}
\]

\[
x = -1 \pm \sqrt{17}
\]

### Final Answer:

\[
x = -1 \pm \sqrt{17}
\]

This matches the second option from your choices: 

\[
x = -1 \pm \sqrt{17}
\]

Would you like further details, or do you have any questions?

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Here are 5 related questions for practice:

1. Solve the quadratic equation \(x^2 - 4x + 4 = 0\).
2. Factor the quadratic expression \(x^2 + 6x + 9 = 0\).
3. Solve \(x^2 + 3x - 10 = 0\) using the quadratic formula.
4. Find the discriminant of the equation \(x^2 - 2x + 1 = 0\).
5. Solve \(2x^2 + 5x - 3 = 0\) by completing the square.

**Tip:** When using the quadratic formula, always calculate the discriminant \(b^2 - 4ac\) first to see if the roots are real, imaginary, or rational.

Solve for x in the equation x squared + 2 x + 1 = 17. x = negative 1 plus-or-minus StartRoot 15 EndRoot x = negative 1 plus-or-minus StartRoot 17 EndRoot x = negative 2 plus-or-minus 2 StartRoot 5 EndRoot

Learn how to solve the quadratic equation x^2 + 2x - 16 = 0 with a step-by-step explanation using the quadratic formula. This example involves finding the roots of the equation and simplifying expressions. Suitable for students in Grades 9-10.

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