3x^2+5x−2=0

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3x^2+5x−2=0

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Identify Coefficients: Step Title: Identify the Coefficients Concise Step Description: Identify the coefficients of the quadratic equation, which are the numbers in front of the variables. In this case, the coefficients are 3, 5, and -2. Step Calculation: Coefficients are 3, 5, -2 Step Output: Coefficients: 3, 5, -2Find Factors: Step Title: Find the Factors Concise Step Description: Find two numbers that multiply to the product of the leading coefficient (3) and the constant term (-2), which is -6, and add to the middle coefficient (5). Step Calculation: Factors of -6 that add up to 5 are 6 and -1. Step Output: Factors: 6, -1Rewrite Middle Term: Step Title: Rewrite the Middle Term Concise Step Description: Rewrite the middle term using the factors found in the previous step. Step Calculation: The quadratic equation can be rewritten as 3x^2 + 6x - x - 2. Step Output: Rewritten Equation: 3x^2 + 6x - x - 2Factor by Grouping: Step Title: Factor by Grouping Concise Step Description: Group the terms into two pairs and factor out the common factors from each pair. Step Calculation: Factor out 3x from the first pair and -1 from the second pair to get 3x(x + 2) - 1(x + 2). Step Output: Factored by Grouping: 3x(x + 2) - 1(x + 2)Factor Out Common Binomial: Step Title: Factor Out the Common Binomial Concise Step Description: Factor out the common binomial (x + 2) from the two terms. Step Calculation: The factored form is (x + 2)(3x - 1). Step Output: Factored Form: (x + 2)(3x - 1)

$3x^2+5x-2=0$

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3x2+5x−2=03x^2+5x-2=03x2+5x−2=0

$3x^2+5x-2=0$