Most Students Get This Wrong 😳

When I first encountered quadratic equations like x² + 2x = 15, I often made the mistake of jumping straight into factoring without rearranging the equation. This almost always led me to wrong answers or confusion. The key, as highlighted in this problem, is to first set the equation to zero: x² + 2x - 15 = 0. Only after this step can you confidently apply factoring methods. For example, with x² + 2x - 15 = 0, you look for two numbers that multiply to -15 and add up to 2, which are 5 and -3. So the factored form is (x + 5)(x - 3) = 0, leading to solutions x = -5 or x = 3. What really helped me master this approach was practicing different quadratic problems by consistently reminding myself to rearrange the terms first. It's tempting when you see x² + 2x = 15 to just try factoring without zero on one side, but this skips a vital algebraic rule. In my experience, understanding why this step matters builds stronger problem-solving habits. If you’re tutoring or self-studying, I recommend writing out the equation and physically moving all terms to one side. This visual aids comprehension and reduces mistakes. Also, don’t hesitate to double-check by plugging your solutions back into the original equation to make sure they satisfy it. This small verification confirms you followed the process correctly. Remember, setting the equation equal to zero sets the stage for all quadratic-solving techniques — whether factoring, completing the square, or using the quadratic formula. Getting comfortable with this step will save you time and frustration in math and build confidence across other algebra topics.