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
Step 1: Gawanya pande zote mbili za mlinganyo kwa mgawo wa x^2, ambao ni 28. 28x^2 + 3x - 1 = 0 (28x^2)/(28) + (3x)/(28) - (1)/(28) = (0)/(28) x^2 + (3)/(28)x - (1)/(28) = 0 Step 2: Hamisha namba isiyo na x (constant term) upande wa kulia wa mlinganyo. x^2 + (3)/(28)x = (1)/(28) Step 3: Kamilisha mraba upande wa kushoto. Ongeza ((1)/(2) × mgawo wa x)^2 pande zote mbili. Mgawo wa x ni (3)/(28). ((1)/(2) × (3)/(28))^2 = ((3)/(56))^2 = (9)/(3136) x^2 + (3)/(28)x + (9)/(3136) = (1)/(28) + (9)/(3136) Step 4: Rahisisha upande wa kulia na andika upande wa kushoto kama mraba kamili. x^2 + (3)/(28)x + (9)/(3136) = (112)/(3136) + (9)/(3136) (x + (3)/(56))^2 = (121)/(3136) Step 5: Chukua mzizi wa mraba pande zote mbili. sqrt((x + (3)/(56))^2) = ±sqrt((121)/(3136)) x + (3)/(56) = ±(11)/(56) Step 6: Tatua kwa x. x = -(3)/(56) ± (11)/(56) Kuna suluhisho mbili: x_1 = -(3)/(56) + (11)/(56) = (8)/(56) = (1)/(7) x_2 = -(3)/(56) - (11)/(56) = -(14)/(56) = -(1)/(4) Majibu ni: x = (1)/(7) au x = -(1)/(4) Tuma swali linalofuata 📸