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
Ili kutafuta thamani ya k ambapo usemi 4x^2 - 12x + 2k + 8 ni mraba kamili, tunahitaji kuhakikisha kuwa sehemu ya mraba kamili inafanana na (ax + b)^2. Step 1: Andika usemi wa mraba kamili. (ax + b)^2 = a^2x^2 + 2abx + b^2 Step 2: Linganisha na 4x^2 - 12x + 2k + 8. • a^2 = 4 a = 2 (chukua thamani chanya) • 2ab = -12 2 · 2 · b = -12 b = -3 Step 3: Tafuta b^2. b^2 = (-3)^2 = 9 Step 4: Linganisha sehemu ya mara kwa mara. b^2 = 2k + 8 9 = 2k + 8 Step 5: Tatua kwa k. 2k = 9 - 8 2k = 1 k = (1)/(2) Thamani ya k ni: (1)/(2) Tuma swali linalofuata 📸