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Solve for x. {:[6x^(2)+60 x+150=0],[x=◻]:}

Solve for x x .\newline6x2+60x+150=0x=□ \begin{array}{l} 6 x^{2}+60 x+150=0 \\ x=\square \end{array}

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Q. Solve for x x .\newline6x2+60x+150=0x=□ \begin{array}{l} 6 x^{2}+60 x+150=0 \\ x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is 6x2+60x+150=06x^2 + 60x + 150 = 0.
  2. Simplify the equation by factoring: Simplify the equation by factoring out the greatest common factor.\newlineThe greatest common factor of the coefficients 6,60,6, 60, and 150150 is 66. We can factor out 66 from each term.\newline6(x2+10x+25)=06(x^2 + 10x + 25) = 0
  3. Set the factored expression equal to zero: Set the factored expression equal to zero to find the solutions for xx.\newlineSince 66 is not equal to zero, we can ignore it for finding the roots and focus on the quadratic expression in the parentheses.\newlinex2+10x+25=0x^2 + 10x + 25 = 0
  4. Factor the quadratic expression: Factor the quadratic expression.\newlineWe need to find two numbers that multiply to 2525 and add up to 1010. The numbers 55 and 55 satisfy these conditions.\newline(x+5)(x+5)=0(x + 5)(x + 5) = 0
  5. Set each factor equal to zero and solve for x: Set each factor equal to zero and solve for x.\newlinex+5=0x + 5 = 0\newlineSubtract 55 from both sides to solve for x.\newlinex=−5x = -5\newlineSince both factors are the same, we only have one unique solution for xx.

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