Recording-2025-03-09T07:20:14.433Z

Word of the Week Mathematically

• The phrase relates to an equation where half of the word squared plus something equals a number.

• Example equation: Word of the week (let's say x) + half of x squared = 36.

Solving the Equation

• Square root both sides of the equation:

  • This yields: ( \sqrt{36} = 6 )

  • Notice it becomes ( x + 4 = \pm 6 )

• Rearranging gives:

  • ( x = 6 - 4 ) or ( x = -6 - 4 )

• Thus, the possible values for x are:

  • Positive Case: ( x = 2 )

  • Negative Case: ( x = -10 )

Factoring and Using the Quadratic Formula

• Factoring can provide answers, including non-integers, if necessary.

• Quadratic Formula: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} )

  • Useful when the equation cannot be factored easily.

• Factors effectively apply even in instances of complex values or irrational numbers, making it a versatile method.