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 3. 3x^2 - 10x + 8 = 0 (3x^2)/(3) - (10x)/(3) + (8)/(3) = (0)/(3) x^2 - (10)/(3)x + (8)/(3) = 0 Step 2: Hamisha namba isiyo na x (constant term) upande wa kulia wa mlinganyo. x^2 - (10)/(3)x = -(8)/(3) Step 3: Kamilisha mraba upande wa kushoto. Ongeza ((1)/(2) × mgawo wa x)^2 pande zote mbili. Mgawo wa x ni -(10)/(3). ((1)/(2) × -(10)/(3))^2 = (-(5)/(3))^2 = (25)/(9) x^2 - (10)/(3)x + (25)/(9) = -(8)/(3) + (25)/(9) Step 4: Rahisisha upande wa kulia na andika upande wa kushoto kama mraba kamili. x^2 - (10)/(3)x + (25)/(9) = -(24)/(9) + (25)/(9) (x - (5)/(3))^2 = (1)/(9) Step 5: Chukua mzizi wa mraba pande zote mbili. sqrt((x - (5)/(3))^2) = ±sqrt((1)/(9)) x - (5)/(3) = ±(1)/(3) Step 6: Tatua kwa x. x = (5)/(3) ± (1)/(3) Kuna suluhisho mbili: x_1 = (5)/(3) + (1)/(3) = (6)/(3) = 2 x_2 = (5)/(3) - (1)/(3) = (4)/(3) Majibu ni: x = 2 au x = (4)/(3) --- Swali la 15: Tatua mlinganyo 2x^2 - 5x - 3 = 0 kwa kukamilisha mraba. Step 1: Gawanya pande zote mbili za mlinganyo kwa mgawo wa x^2, ambao ni 2. 2x^2 - 5x - 3 = 0 (2x^2)/(2) - (5x)/(2) - (3)/(2) = (0)/(2) x^2 - (5)/(2)x - (3)/(2) = 0 Step 2: Hamisha namba isiyo na x (constant term) upande wa kulia wa mlinganyo. x^2 - (5)/(2)x = (3)/(2) Step 3: Kamilisha mraba upande wa kushoto. Ongeza ((1)/(2) × mgawo wa x)^2 pande zote mbili. Mgawo wa x ni -(5)/(2). ((1)/(2) × -(5)/(2))^2 = (-(5)/(4))^2 = (25)/(16) x^2 - (5)/(2)x + (25)/(16) = (3)/(2) + (25)/(16) Step 4: Rahisisha upande wa kulia na andika upande wa kushoto kama mraba kamili. x^2 - (5)/(2)x + (25)/(16) = (24)/(16) + (25)/(16) (x - (5)/(4))^2 = (49)/(16) Step 5: Chukua mzizi wa mraba pande zote mbili. sqrt((x - (5)/(4))^2) = ±sqrt((49)/(16)) x - (5)/(4) = ±(7)/(4) Step 6: Tatua kwa x. x = (5)/(4) ± (7)/(4) Kuna suluhisho mbili: x_1 = (5)/(4) + (7)/(4) = (12)/(4) = 3 x_2 = (5)/(4) - (7)/(4) = -(2)/(4) = -(1)/(2) Majibu ni: x = 3 au x = -(1)/(2) --- Swali la 16: Tatua mlinganyo x^2 - 6x + 5 = 0 kwa kukamilisha mraba. Step 1: Hamisha namba isiyo na x (constant term) upande wa kulia wa mlinganyo. x^2 - 6x = -5 Step 2: Kamilisha mraba upande wa kushoto. Ongeza ((1)/(2) × mgawo wa x)^2 pande zote mbili. Mgawo wa x ni -6. ((1)/(2) × -6)^2 = (-3)^2 = 9 x^2 - 6x + 9 = -5 + 9 Step 3: Rahisisha upande wa kulia na andika upande wa kushoto kama mraba kamili. (x - 3)^2 = 4 Step 4: Chukua mzizi wa mraba pande zote mbili. sqrt((x - 3)^2) = ±sqrt(4) x - 3 = ± 2 Step 5: Tatua kwa x. x = 3 ± 2 Kuna suluhisho mbili: x_1 = 3 + 2 = 5 x_2 = 3 - 2 = 1 Majibu ni: x = 5 au x = 1 That's 2 down. 3 left today — send the next one.