Identify Structure of Expression: Step Title: Identify the Structure of the ExpressionConcise Step Description: Recognize that the given expression is a quadratic in terms of c2.Step Calculation: The expression is in the form of a quadratic equation, where the variable is c2 instead of c.Step Output: The expression is a quadratic in c2.
Identify Coefficients: Step Title: Identify the CoefficientsConcise Step Description: Identify the coefficients of the quadratic equation in terms of c2.Step Calculation: Coefficients are 121, −44, and 4.Step Output: Coefficients: 121, −44, 4
Find Factors: Step Title: Find the FactorsConcise Step Description: Find two numbers that multiply to 4 (the last term) and add to −44 (the coefficient of the middle term), considering the first term coefficient is 121.Step Calculation: Factors of 4 that add up to −44 when multiplied by 121 are −2 and −2 (since 121×4=484, and we need two numbers that multiply to 484 and add up to −44).Step Output: Factors: −2, −2
Write Factored Form: Step Title: Write the Factored FormConcise Step Description: Write the factored form of the quadratic equation using the factors found in the previous step.Step Calculation: The factored form is (11c2−2)(11c2−2), which is a perfect square trinomial.Step Output: Factored Form: (11c2−2)2