How do i solve for the variable
3x= sqrt5x+1
To solve for the variable in the equation 3x = √(5x + 1), you need to isolate the variable x on one side of the equation. Here's a step-by-step process to solving the equation:
Step 1: Square both sides of the equation to eliminate the square root on the right side. This gives us:
(3x)² = (√(5x + 1))²
Simplifying further, we have:
9x² = 5x + 1
Step 2: Rearrange the equation to bring all the terms to one side:
9x² - 5x - 1 = 0
Step 3: This quadratic equation can be solved using various methods. One common method is factoring, but in this case, factoring might not easily lead to rational solutions. So, we'll use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In our equation, a = 9, b = -5, and c = -1. Plugging these values into the quadratic formula, we get:
x = (-(-5) ± √((-5)² - 4 * 9 * (-1))) / (2 * 9)
Simplifying further:
x = (5 ± √(25 + 36)) / 18
x = (5 ± √61) / 18
Hence, the two possible solutions for x are:
x = (5 + √61) / 18
x = (5 - √61) / 18