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(2x+1)^(2)+(x+1)^(2)=6x+47

(2x+1)2+(x+1)2=6x+47 (2 x+1)^{2}+(x+1)^{2}=6 x+47

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Full solution

Q. (2x+1)2+(x+1)2=6x+47 (2 x+1)^{2}+(x+1)^{2}=6 x+47
  1. Expand First Term: Expand the first term (2x+1)2(2x+1)^{2} using the formula (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2.\newlineCalculation: (2x+1)2=4x2+4x+1(2x+1)^{2} = 4x^2 + 4x + 1.
  2. Expand Second Term: Expand the second term (x+1)2(x+1)^{2} using the same formula.\newlineCalculation: (x+1)2=x2+2x+1(x+1)^{2} = x^2 + 2x + 1.
  3. Add Expanded Forms: Add the expanded forms of (2x+1)2(2x+1)^{2} and (x+1)2(x+1)^{2}.\newlineCalculation: 4x2+4x+1+x2+2x+14x^2 + 4x + 1 + x^2 + 2x + 1.
  4. Combine Like Terms: Combine like terms on the left side of the equation.\newlineCalculation: 5x2+6x+25x^2 + 6x + 2.
  5. Set Equation Equal: Set the equation equal to 6x+476x + 47.\newlineCalculation: 5x2+6x+2=6x+475x^2 + 6x + 2 = 6x + 47.
  6. Subtract and Set Zero: Subtract 6x6x and 4747 from both sides to set the equation to zero.\newlineCalculation: 5x2+6x+2−6x−47=05x^2 + 6x + 2 - 6x - 47 = 0.
  7. Combine Like Terms: Combine like terms on the left side after subtraction.\newlineCalculation: 5x2−45=05x^2 - 45 = 0.

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