What is 'x'?

When you encounter an algebraic equation involving 'x', such as the example 7x + 49 = x x, the goal is to determine the value of 'x' that makes the equation true. In algebra, 'x' is often used as a variable representing an unknown number. To solve equations like 7x + 49 = x x, you first need to understand how to manipulate terms. The equation can be interpreted differently depending on whether the symbol 'x' between the two sides represents multiplication or equals sign placement mistakes. Usually, in proper notation, it would be written as 7x + 49 = x^2 or a similar form. Assuming the equation meant is 7x + 49 = x^2, solving involves rearranging the expression: 1. Bring all terms to one side to form a quadratic equation: x^2 - 7x - 49 = 0. 2. Use the quadratic formula x = [-b ± √(b² - 4ac)] / 2a, where a=1, b=-7, c=-49. 3. Calculate the discriminant: b² - 4ac = (-7)² - 4(1)(-49) = 49 + 196 = 245. 4. Find the square root of 245, which is approximately 15.65. 5. Calculate the two possible values for x: - x = (7 + 15.65) / 2 = 22.65 / 2 ≈ 11.33 - x = (7 - 15.65) / 2 = -8.65 / 2 ≈ -4.33 So, the two values of x that satisfy the equation are approximately 11.33 and -4.33. This type of problem is common in high school mathematics and fundamental to understanding algebra principles. Mastering these techniques helps with coursework, standardized tests, and practical applications of math. If the equation or context is different, clarifying the exact problem statement is vital. For example, if the 'x x' in the OCR text refers to a typo or symbol mix-up, reformatting the equation or asking for more details would enable a proper solution. Overall, learning algebraic problem solving improves logical reasoning and numerical proficiency, essential skills for students and helpful for educators assisting learners in subjects like math and science.