Two consecutive odd integers have a product of 99 solve with a quadratic equation and find images

Answer:9 and 11OR-9 and -11Step-by-step explanation:let x be the one odd integerThe pattern of numbers go: odd - even - odd - evenThe next consecutive odd integer would be x + 2"Product" means multiplying. Write "the product of two consecutive odd integers with a product of 99" as an algebraic statement:x(x+2)=99                Distribute over bracketsx² + 2x = 99              Rearrange the equal 0x² + 2x - 99 = 0Remember a quadratic equation is ax² + bx + c = 0  (Equate to 0 to use quadratic formula)State values for quadratic formula from simplified quadratic equationa = 1; b = 2; c = -99Use the quadratic formula.[tex]x=\frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]Substitute the values of "a", "b", and "c"[tex]x=\frac{-2±\sqrt{2^{2}-4(1)(-99)}}{2(1)}[/tex]               Simplify[tex]x=\frac{-2±\sqrt{400}}{2}[/tex]                    Solve the root[tex]x=\frac{-2±20}{2}[/tex]Split the equation at the ± [tex]x=\frac{-2+20}{2}[/tex][tex]x=\frac{18}{2}[/tex]x = 9                 Possible integer solution[tex]x=\frac{-2-20}{2}[/tex][tex]x=\frac{-22}{2}[/tex]x = -11                   Possible integer solutionIntegers include all positive and negative whole numbers, and 0. Both positive and negative answers are possible in this problem.Use "x+2" to get the consecutive integer from the initial possible values for "x".If x = 9:x+2 = x+9 = 119 and 11If x = -11:x+2 = -11+2 = -9-9 and -11See if your answers make sense:9 X 11 = 99-9 X -11 = 99Both are possible solutions.