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(4x-5)(4x+5)-(4x-1)^(2)=9-2x

22) (4x−5)(4x+5)−(4x−1)2=9−2x (4 x-5)(4 x+5)-(4 x-1)^{2}=9-2 x

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Full solution

Q. 22) (4x−5)(4x+5)−(4x−1)2=9−2x (4 x-5)(4 x+5)-(4 x-1)^{2}=9-2 x
  1. Apply difference of squares: Step 11: Apply the difference of squares formula to (4x−5)(4x+5)(4x-5)(4x+5).(4x−5)(4x+5)=(4x)2−(5)2=16x2−25(4x-5)(4x+5) = (4x)^2 - (5)^2 = 16x^2 - 25
  2. Expand (4x−1)2(4x-1)^2: Step 22: Expand (4x−1)2(4x-1)^2.(4x−1)2=(4x−1)(4x−1)=16x2−8x+1(4x-1)^2 = (4x-1)(4x-1) = 16x^2 - 8x + 1
  3. Subtract squared terms: Step 33: Subtract (4x−1)2(4x-1)^2 from (4x−5)(4x+5)(4x-5)(4x+5).\newline16x2−25−(16x2−8x+1)16x^2 - 25 - (16x^2 - 8x + 1)\newline= 16x2−25−16x2+8x−116x^2 - 25 - 16x^2 + 8x - 1\newline= 8x−268x - 26
  4. Simplify expression: Step 44: Simplify 9−2x9 - 2x. 9−2x9 - 2x
  5. Compare and solve: Step 55: Compare 8x−268x - 26 with 9−2x9 - 2x.\newline8x−26=9−2x8x - 26 = 9 - 2x\newline8x+2x=9+268x + 2x = 9 + 26\newline10x=3510x = 35\newlinex=x = 33.55$

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