Question

Solve the following quadratic equation for all values of xx in simplest form.
2, left parenthesis, x, plus, 4, right parenthesis, squared, plus, 44, equals, 46
2(x+4)
2
+44=
46

Answer 1

To solve the equation \( 2(x + 4)^2 + 44 = 46 \), we will first isolate the squared term.

1. Subtract 44 from both sides:
\[
2(x + 4)^2 + 44 - 44 = 46 - 44
\]
which simplifies to:
\[
2(x + 4)^2 = 2
\]

2. Next, divide both sides by 2:
\[
(x + 4)^2 = 1
\]

3. Now, take the square root of both sides. Remember to consider both the positive and negative square roots:
\[
x + 4 = 1 \quad \text{or} \quad x + 4 = -1
\]

4. Solve for \( x \) in both cases:
- For the first equation:
\[
x + 4 = 1 \\
x = 1 - 4 \\
x = -3
\]

- For the second equation:
\[
x + 4 = -1 \\
x = -1 - 4 \\
x = -5
\]

The solutions to the quadratic equation are:
\[
x = -3 \quad \text{and} \quad x = -5
\]