Solve the equation 3x2 - 17x - 6 = 0 using factorization method

July 30, 2026Mathematics

ScanSolve AI Answer

July 30, 2026

Answer

Step 1: Andika nambari zote kama nguvu za 2. $32 = 2^5$ $8 = 2^3$ $64 = 2^6$

Step 2: Badilisha nambari hizi kwenye mlinganyo. $(2^5)^{(x-3)} \div (2^3)^{(x-4)} = 2^6 \div 2^x$

Step 3: Tumia sheria ya nguvu $(a^m)^n = a^{mn}$ . $2^{5(x-3)} \div 2^{3(x-4)} = 2^6 \div 2^x$ $2^{5x-15} \div 2^{3x-12} = 2^6 \div 2^x$

Step 4: Tumia sheria ya kugawanya $a^m \div a^n = a^{m-n}$ . $2^{(5x-15) - (3x-12)} = 2^{6-x}$ $2^{5x-15-3x+12} = 2^{6-x}$ $2^{2x-3} = 2^{6-x}$

Step 5: Linganisha viashiria vya nguvu kwa sababu besi ni sawa. $2x-3 = 6-x$

Step 6: Tatua kwa $x$ . $2x+x = 6+3$ $3x = 9$ $x = \frac{9}{3}$ $x = \textbf{3}$

Tuma swali linalofuata 📸

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Quick Answer

Andika nambari zote kama nguvu za 2. 32 = 2^5 8 = 2^3 64 = 2^6 Step 2: Badilisha nambari hizi kwenye mlinganyo.

Asked on July 30, 2026Mathematics

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 AnswerAnswered on July 30, 2026

Step 1: Andika nambari zote kama nguvu za 2. 32 = 2^5 8 = 2^3 64 = 2^6 Step 2: Badilisha nambari hizi kwenye mlinganyo. (2^5)^(x-3) ÷ (2^3)^(x-4) = 2^6 ÷ 2^x Step 3: Tumia sheria ya nguvu (a^m)^n = a^mn. 2^5(x-3) ÷ 2^3(x-4) = 2^6 ÷ 2^x 2^5x-15 ÷ 2^3x-12 = 2^6 ÷ 2^x Step 4: Tumia sheria ya kugawanya a^m ÷ a^n = a^m-n. 2^(5x-15) - (3x-12) = 2^6-x 2^5x-15-3x+12 = 2^6-x 2^2x-3 = 2^6-x Step 5: Linganisha viashiria vya nguvu kwa sababu besi ni sawa. 2x-3 = 6-x Step 6: Tatua kwa x. 2x+x = 6+3 3x = 9 x = (9)/(3) x = 3 Tuma swali linalofuata 📸

Asked on July 30, 2026Mathematics

ScanSolve AI AnswerAnswered on July 30, 2026

Step 1: Andika nambari zote kama nguvu za 2. 32 = 2^5 8 = 2^3 64 = 2^6 Step 2: Badilisha nambari hizi kwenye mlinganyo. (2^5)^(x-3) ÷ (2^3)^(x-4) = 2^6 ÷ 2^x Step 3: Tumia sheria ya nguvu (a^m)^n = a^mn. 2^5(x-3) ÷ 2^3(x-4) = 2^6 ÷ 2^x 2^5x-15 ÷ 2^3x-12 = 2^6 ÷ 2^x Step 4: Tumia sheria ya kugawanya a^m ÷ a^n = a^m-n. 2^(5x-15) - (3x-12) = 2^6-x 2^5x-15-3x+12 = 2^6-x 2^2x-3 = 2^6-x Step 5: Linganisha viashiria vya nguvu kwa sababu besi ni sawa. 2x-3 = 6-x Step 6: Tatua kwa x. 2x+x = 6+3 3x = 9 x = (9)/(3) x = 3 Tuma swali linalofuata 📸