Can you solve this?

The equation presented, √(2x + 2) = √(10x - 4), involves solving for x within square root functions, which is a common type of radical equation in algebra. Radical equations usually require isolating the radicals and squaring both sides carefully to eliminate the square roots, followed by solving the resulting polynomial equation. To solve this equation, first ensure the expressions inside the radicals are defined since the radicands (the expressions under the square root) must be non-negative. Step 1: Identify the domain For √(2x + 2), require 2x + 2 ≥ 0 which means x ≥ -1. For √(10x - 4), require 10x - 4 ≥ 0 which means x ≥ 0.4. The domain for the equation is therefore x ≥ 0.4. Step 2: Square both sides (√(2x + 2))² = (√(10x - 4))² ⟹ 2x + 2 = 10x - 4 Step 3: Rearrange terms 2x + 2 = 10x - 4 2 + 4 = 10x - 2x 6 = 8x Step 4: Solve for x x = 6 / 8 = 3/4 = 0.75 Step 5: Check the solution Verify that x = 0.75 lies in the domain (x ≥ 0.4) and substitute back to original equation: √(2(0.75) + 2) = √(1.5 + 2) = √3.5 ≈ 1.87 √(10(0.75) - 4) = √(7.5 - 4) = √3.5 ≈ 1.87 Both sides equal, so x = 0.75 is the valid solution. Understanding how to approach equations involving radicals helps strengthen algebra skills and prepares for more advanced math problems. The key is managing domain restrictions and carefully performing algebraic manipulations to avoid extraneous solutions. This problem aligns with typical high school and college preparatory math curricula and supports learning objectives for solving equations involving square roots.