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Solve for x. {:[x^(2)+10 x+25=0],[x=]:}

Solve for x x .\newlinex2+10x+25=0x=□ \begin{array}{l} x^{2}+10 x+25=0 \\ x=\square \end{array}

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Q. Solve for x x .\newlinex2+10x+25=0x=□ \begin{array}{l} x^{2}+10 x+25=0 \\ x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to be solved.\newlineWe are given the quadratic equation x2+10x+25=0x^2 + 10x + 25 = 0. We need to find the values of xx that satisfy this equation.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to 2525 and add up to 1010. The numbers 55 and 55 meet these criteria because 5×5=255 \times 5 = 25 and 5+5=105 + 5 = 10.\newlineSo, we can write the equation as (x+5)(x+5)=0(x + 5)(x + 5) = 0.
  3. Set each factor equal to zero: Set each factor equal to zero and solve for xx.\newlineSince (x+5)(x+5)=0(x + 5)(x + 5) = 0, we can set each factor equal to zero and solve for xx.\newlinex+5=0x + 5 = 0\newlineSubtract 55 from both sides to solve for xx.\newlinex=−5x = -5
  4. Check for other possible solutions: Check for any other possible solutions.\newlineSince both factors are the same, (x+5)(x + 5), we only have one unique solution for xx.\newlinex=−5x = -5

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