This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Huu hapa utatuzi wa mlinganyo 2x^2 + 7x - 9 = 0 kwa kutumia njia ya kukamilisha mraba: Step 1: Gawanya pande zote mbili za mlinganyo kwa mgawo wa x^2, ambao ni 2. (2x^2)/(2) + (7x)/(2) - (9)/(2) = (0)/(2) x^2 + (7)/(2)x - (9)/(2) = 0 Step 2: Hamisha nambari isiyobadilika (constant term) kwenda upande wa kulia wa mlinganyo. x^2 + (7)/(2)x = (9)/(2) Step 3: Kamilisha mraba kwa kuongeza ((b)/(2))^2 kwa pande zote mbili. Katika mlinganyo huu, b = (7)/(2). ((b)/(2))^2 = ((7/2)/(2))^2 = ((7)/(4))^2 = (49)/(16) Ongeza (49)/(16) kwa pande zote mbili: x^2 + (7)/(2)x + (49)/(16) = (9)/(2) + (49)/(16) Step 4: Andika upande wa kushoto kama mraba kamili na rahisha upande wa kulia. (x + (7)/(4))^2 = (72)/(16) + (49)/(16) (x + (7)/(4))^2 = (121)/(16) Step 5: Chukua mzizi wa mraba wa pande zote mbili. sqrt((x + (7)/(4))^2) = ±sqrt((121)/(16)) x + (7)/(4) = ±(11)/(4) Step 6: Tatua kwa x kwa kutenganisha kesi mbili (chanya na hasi). Kesi ya kwanza: x + (7)/(4) = (11)/(4) x = (11)/(4) - (7)/(4) x = (4)/(4) x = 1 Kesi ya pili: x + (7)/(4) = -(11)/(4) x = -(11)/(4) - (7)/(4) x = -(18)/(4) x = -(9)/(2) Majibu ni: x = 1 au x = -(9)/(2) Tuma swali linalofuata 📸