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Rewrite the equation by completing the square. {:[2x^(2)+7x+6=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newline2x2+7x+6=02x^{2}+7x+6=0\newline(x+□)2=□(x+\square)^{2}=\square

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Full solution

Q. Rewrite the equation by completing the square.\newline2x2+7x+6=02x^{2}+7x+6=0\newline(x+□)2=□(x+\square)^{2}=\square
  1. Given quadratic equation: Start with the given quadratic equation. 2x2+7x+6=02x^2 + 7x + 6 = 0
  2. Divide by coefficient of x2x^2: Divide all terms by the coefficient of x2x^2 to make the coefficient of x2x^2 equal to 11.\newlinex2+(72)x+3=0x^2 + \left(\frac{7}{2}\right)x + 3 = 0
  3. Move constant term to right side: Move the constant term to the right side of the equation. x2+(72)x=−3x^2 + \left(\frac{7}{2}\right)x = -3
  4. Complete the square: Find the number to complete the square. Take half of the coefficient of xx, square it, and add it to both sides of the equation.\newline(74)2=4916\left(\frac{7}{4}\right)^2 = \frac{49}{16}\newlinex2+(72)x+4916=−3+4916x^2 + \left(\frac{7}{2}\right)x + \frac{49}{16} = -3 + \frac{49}{16}
  5. Convert right side to common denominator: Convert the right side to have a common denominator before combining the terms.\newline−3+4916=−4816+4916=116-3 + \frac{49}{16} = -\frac{48}{16} + \frac{49}{16} = \frac{1}{16}\newlinex2+(72)x+4916=116x^2 + \left(\frac{7}{2}\right)x + \frac{49}{16} = \frac{1}{16}
  6. Write left side as perfect square: Write the left side of the equation as a perfect square. (x+74)2=116(x + \frac{7}{4})^2 = \frac{1}{16}

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