To solve the equation [tex]\(5x^2 + 3 = 83\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Simplify the Equation:
[tex]\[
5x^2 + 3 = 83
\][/tex]
Subtract 3 from both sides to isolate the quadratic term:
[tex]\[
5x^2 = 80
\][/tex]
2. Divide by 5:
Divide both sides of the equation by 5 to simplify:
[tex]\[
x^2 = 16
\][/tex]
3. Take the Square Root:
To solve for [tex]\(x\)[/tex], take the square root of both sides. Remember that the square root operation yields both positive and negative roots:
[tex]\[
x = \pm \sqrt{16}
\][/tex]
4. Simplify the Square Root:
The square root of 16 is 4, so:
[tex]\[
x = \pm 4
\][/tex]
Therefore, the solutions are:
[tex]\[
x = -4 \quad \text{and} \quad x = 4
\][/tex]
When entering the solutions from least to greatest, we have:
[tex]\[
\text{lesser } x = -4
\][/tex]
[tex]\[
\text{greater } x = 4
\][/tex]
