Solving a radical equation.
Begin with an equation you know to be true such as \(3+5 = 8\).
Try the following:
- Square each of the three numbers in the equation. Is the equation still true?
- Square each side of the equation (square the sum of three and five). Is the equation still true?
Take what you learned about keeping the numerical equation true to solve the equations below.
Solve the following two equations by isolating the radical on one side and squaring both sides. Check to be sure the solutions actually work by substituting the solution into the equation.
i. \( \sqrt{2x+1}-5 = -2\)
ii. \( \sqrt{2x+1}+5 = 2\)
Check your solutions.
