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Solve for x. {:[5x^(2)+70 x+245=0],[x=◻]:}

Solve for x x .\newline5x2+70x+245=0x=□ \begin{array}{l} 5 x^{2}+70 x+245=0 \\ x=\square \end{array}

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Q. Solve for x x .\newline5x2+70x+245=0x=□ \begin{array}{l} 5 x^{2}+70 x+245=0 \\ x=\square \end{array}
  1. Write Quadratic Equation: Write down the quadratic equation.\newlineWe have the quadratic equation 5x2+70x+245=05x^2 + 70x + 245 = 0.
  2. Factor Out GCF: Factor out the greatest common factor (GCF) if possible.\newlineIn this case, we can factor out 55 from each term.\newline5(x2+14x+49)=05(x^2 + 14x + 49) = 0
  3. Set Equation Equal to Zero: Set the factored equation equal to zero and solve for xx.\newlineNow we have a simpler quadratic equation: x2+14x+49=0x^2 + 14x + 49 = 0.\newlineWe need to find two numbers that multiply to 4949 and add up to 1414.
  4. Factor the Quadratic Equation: Factor the quadratic equation.\newlineThe numbers that multiply to 4949 and add up to 1414 are 77 and 77.\newlineSo we can write the equation as (x+7)(x+7)=0(x + 7)(x + 7) = 0, which is also (x+7)2=0(x + 7)^2 = 0.
  5. Solve for x: Solve for x.\newlineSince (x+7)2=0(x + 7)^2 = 0, we can take the square root of both sides to get x+7=0x + 7 = 0.\newlineSubtracting 77 from both sides gives us x=−7x = -7.

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