To find the roots of the equation [tex]\((x + 7)^2 = 49\)[/tex], we can follow these steps:
1. Start by recognizing that [tex]\((x + 7)^2 = 49\)[/tex] is a quadratic equation. To solve for [tex]\(x\)[/tex], we'll first need to take the square root on both sides of the equation.
2. Taking the square root of both sides, we get:
[tex]\[
x + 7 = \pm \sqrt{49}
\][/tex]
3. The square root of 49 is 7. Therefore, we can rewrite the equation as:
[tex]\[
x + 7 = \pm 7
\][/tex]
4. This gives us two separate equations to solve for [tex]\(x\)[/tex]:
[tex]\[
x + 7 = 7 \quad \text{and} \quad x + 7 = -7
\][/tex]
5. Solving the first equation [tex]\(x + 7 = 7\)[/tex]:
[tex]\[
x + 7 = 7
\][/tex]
Subtract 7 from both sides:
[tex]\[
x = 0
\][/tex]
6. Solving the second equation [tex]\(x + 7 = -7\)[/tex]:
[tex]\[
x + 7 = -7
\][/tex]
Subtract 7 from both sides:
[tex]\[
x = -14
\][/tex]
7. Therefore, the roots of the equation [tex]\((x + 7)^2 = 49\)[/tex] are:
[tex]\[
x = \{0, -14\}
\][/tex]
Hence, the roots of the equation [tex]\((x + 7)^2 = 49\)[/tex] are [tex]\(0.0\)[/tex] and [tex]\(-14.0\)[/tex].
