To solve the given quadratic equation [tex]\(18 - x^2 = 13\)[/tex], follow these steps:
1. Isolate the quadratic term:
Begin by moving the constant term on the right-hand side of the equation to the left-hand side to set the equation to zero.
[tex]\[
18 - x^2 - 13 = 0
\][/tex]
2. Simplify the equation:
Combine the like terms on the left-hand side.
[tex]\[
5 - x^2 = 0
\][/tex]
3. Isolate [tex]\(x^2\)[/tex]:
Move [tex]\(x^2\)[/tex] to the right-hand side by adding [tex]\(x^2\)[/tex] to both sides of the equation.
[tex]\[
5 = x^2
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Take the square root of both sides of the equation to isolate [tex]\(x\)[/tex]. Remember that taking the square root of a number results in both a positive and a negative solution.
[tex]\[
x = \pm \sqrt{5}
\][/tex]
5. Write the solutions:
The solutions to the equation are:
[tex]\[
x = \sqrt{5} \quad \text{and} \quad x = -\sqrt{5}
\][/tex]
In decimal form, these solutions are approximately:
[tex]\[
x \approx 2.23606797749979 \quad \text{and} \quad x \approx -2.23606797749979
\][/tex]
Thus, the solutions to the quadratic equation [tex]\(18 - x^2 = 13\)[/tex] are [tex]\(x \approx 2.23606797749979\)[/tex] and [tex]\(x \approx -2.23606797749979\)[/tex].
