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Solve for x. {:[5x^(2)+60 x+180=0],[x=◻]:}

Solve for x x .\newline5x2+60x+180=0x=□ \begin{array}{l} 5 x^{2}+60 x+180=0 \\ x=\square \end{array}

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Full solution

Q. Solve for x x .\newline5x2+60x+180=0x=□ \begin{array}{l} 5 x^{2}+60 x+180=0 \\ x=\square \end{array}
  1. Write Equation: Write down the given quadratic equation.\newlineThe equation given is 5x2+60x+180=05x^2 + 60x + 180 = 0.
  2. Factor GCF: Factor out the greatest common factor (GCF) if possible.\newlineIn this case, we can factor out 55 from each term.\newline5(x2+12x+36)=05(x^2 + 12x + 36) = 0
  3. Simplify Equation: Now we have a simpler quadratic equation to solve: x2+12x+36=0x^2 + 12x + 36 = 0.\newlineWe need to find two numbers that multiply to 3636 and add up to 1212.\newlineThe numbers 66 and 66 fit this requirement because 6×6=366 \times 6 = 36 and 6+6=126 + 6 = 12.
  4. Find Numbers: Write the factored form of the quadratic equation using the numbers found in Step 33.\newline(x+6)(x+6)=0(x + 6)(x + 6) = 0
  5. Write Factored Form: Set each factor equal to zero and solve for xx.x+6=0x + 6 = 0Subtract 66 from both sides to solve for xx.x=−6x = -6Since both factors are the same, we only get one solution for xx.

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