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Using the quadratic formula, I found the solution set is x=2,x=-9
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An open statement is a sentence that contains a variable , such as x. The solution set for an open sentence is the set of values that when substituted for the variable make a true statement. The members of the solution set are called solutions. Examples: x = 2. Solution set is {2} solution is 2. x2 - 5 = 4 Solution set is {-3, 3 } solutions are -3 and 3. x > 0 Solution set = {x " x > 0 } That is all positive numbers. Every positive number is a solution. There are some finer points that I did not mention such as the possibility of more than one variable and limitations on the values that allowed in the substitutions.
Given the equation x2 - x - 20 = 0, we see that it can likely be factored easily. Through simple trial and error we find that: (x - 5)(x + 4) = 0. From here, we set both terms equal to zero to find all possible solutions. x - 5 = 0 x = 5 and x + 4 = 0 x = -4. Substituting 5 and -4 back into the original equation yield true results. Thus the solution set is x = -4, 5. More formal, the solution set is {-4, 5}. Note: There are other methods of solving this problem such as the quadratic formula or by graphing the function.
x - x2 - 9x + 14 = 0 ; whence, x2 + 8x = 14 , x2 + 8x + 16 = 30 , and x + 4 = ±√30 . Therefore, x = ±√30 - 4 .