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Solve the equation:
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Q. Solve the equation:
- Identify Coefficients: Step Title: Identify the CoefficientsConcise Step Description: Identify the coefficients of the quadratic equation, which are the numbers in front of the variables. In this case, the coefficients are , , and .Step Calculation: Coefficients are , , Step Output: Coefficients: , ,
- Find Factors: Step Title: Find the FactorsConcise Step Description: Find two numbers that multiply to the product of the leading coefficient and the constant term , which is , and add to the middle coefficient .Step Calculation: Factors of that add up to are and .Step Output: Factors: ,
- Rewrite Middle Term: Step Title: Rewrite the Middle TermConcise Step Description: Rewrite the middle term using the factors found in the previous step.Step Calculation: The quadratic equation can be rewritten as .Step Output: Rewritten Equation:
- Factor by Grouping: Step Title: Factor by GroupingConcise Step Description: Group the terms into two pairs and factor out the common factors from each pair.Step Calculation: Factor out from the first pair and from the second pair to get .Step Output: Factored by Grouping:
- Factor Out Binomial: Step Title: Factor Out the Common BinomialConcise Step Description: Factor out the common binomial factor from the two groups.Step Calculation: The common binomial factor is , so the factored form is .Step Output: Factored Form:
