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.
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Tunatakiwa kutatua mlinganyo wa quadratic x^2 - 12x + 10 = 0 kwa kutumia njia ya kukamilisha mraba. Step 1: Hamisha namba isiyo na x (constant term) upande wa kulia wa mlinganyo. x^2 - 12x = -10 Step 2: Ili kukamilisha mraba upande wa kushoto, chukua nusu ya mgawo wa x (ambayo ni -12), kisha ipandishe mraba. Mgawo wa x ni -12. Nusu ya -12 ni (-12)/(2) = -6. Mraba wa -6 ni (-6)^2 = 36. Step 3: Ongeza namba hii (36) pande zote mbili za mlinganyo. x^2 - 12x + 36 = -10 + 36 x^2 - 12x + 36 = 26 Step 4: Andika upande wa kushoto kama mraba kamili. (x - 6)^2 = 26 Step 5: Chukua mzizi wa mraba pande zote mbili za mlinganyo. Kumbuka kuwa kuna majibu mawili, chanya na hasi. sqrt((x - 6)^2) = ±sqrt(26) x - 6 = ±sqrt(26) Step 6: Tatua kwa x kwa kuongeza 6 pande zote mbili. x = 6 ±sqrt(26) Hivyo, mizizi ya mlinganyo ni: x_1 = 6 + sqrt(26) x_2 = 6 - sqrt(26) Majibu ya mwisho ni: x = 6 ± sqrt(26) Tuma swali linalofuata 📸