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Solve for x. {:[x^(2)+14 x+49=0],[x=◻]:}

Solve for x x .\newlinex2+14x+49=0x=□ \begin{array}{l} x^{2}+14 x+49=0 \\ x=\square \end{array}

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Q. Solve for x x .\newlinex2+14x+49=0x=□ \begin{array}{l} x^{2}+14 x+49=0 \\ x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is x2+14x+49=0x^2 + 14x + 49 = 0.\newlineWe need to find the values of xx that satisfy this equation.
  2. Recognize the structure: Recognize the structure of the quadratic equation.\newlineThe equation x2+14x+49=0x^2 + 14x + 49 = 0 is a perfect square trinomial because 4949 is the square of 77 and 1414 is twice the product of 77.
  3. Factor the perfect square trinomial: Factor the perfect square trinomial.\newlineSince (x+7)2=x2+14x+49(x + 7)^2 = x^2 + 14x + 49, we can write the equation as (x+7)2=0(x + 7)^2 = 0.
  4. Solve the factored equation: Solve the factored equation.\newlineSet the factored expression equal to zero: (x+7)2=0(x + 7)^2 = 0.\newlineTake the square root of both sides: x+7=0x + 7 = 0.
  5. Find the value of x: Find the value of xx.\newlineSubtract 77 from both sides to solve for xx: x=−7x = -7.

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