Solve the equation x^2 + 3x - 10 = 0
Identify a, b and c based in the GENERAL FORM OF A QUADRATIC EQUATION: ax2 + bx + c (= 0)ax2 + bx + c = 0 x2 + 3x - 10 = 0, so a = 1, b = 3 and c = -10Rule 1: List factors of c in pairs [Factors of 10 are (1 & 10) and (2 & 5)]Rule 2: The sign of c indicates if the factors are the same sign [when c is positive, (++ or --)] or different signs [when c is negative, (+-)] Rule 3: Choose the pair of factors that when subjected to these two rules, add to make b.Thus, in this example, the factors are different signs, with the largest factor being positive. 5 - 2 = 3, meaning the pairing of 5 & -2 abides by all 3 rules. Therefore(x + 5)(x - 2) = 0This means (x + 5) = 0 or (x - 2) = 0, so x = 2 or -5.CHECK BACK by substituting into the original equation.22 + 3(2) - 10 = 4 + 6 - 10 = 0 ✔52 + 3(-5) -10 = 25 - 15 -10 = 0 ✔
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