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Solve for x. {:[6x^(2)+36 x+54=0],[x=◻]:}

Solve for x x .\newline6x2+36x+54=0x=□ \begin{array}{l} 6 x^{2}+36 x+54=0 \\ x=\square \end{array}

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Full solution

Q. Solve for x x .\newline6x2+36x+54=0x=□ \begin{array}{l} 6 x^{2}+36 x+54=0 \\ x=\square \end{array}
  1. Factor out GCF: First, we observe the given quadratic equation: 6x2+36x+54=06x^2 + 36x + 54 = 0. To simplify, we can factor out the greatest common factor (GCF), which is 66 in this case.\newlineCalculation: 6(x2+6x+9)=06(x^2 + 6x + 9) = 0
  2. Solve quadratic equation: Next, we need to solve the equation inside the parentheses: x2+6x+9=0x^2 + 6x + 9 = 0. This is a quadratic equation in standard form.\newlineNo calculation in this step, just setting up for the next step.
  3. Use quadratic formula or factor: To solve the quadratic equation x2+6x+9=0x^2 + 6x + 9 = 0, we can use the quadratic formula, x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a=1a = 1, b=6b = 6, and c=9c = 9. However, noticing that the equation x2+6x+9=0x^2 + 6x + 9 = 0 can be factored as (x+3)2=0(x + 3)^2 = 0, we can solve it more directly.
  4. Find the solution: Since (x+3)2=0(x + 3)^2 = 0, we find that x+3=0x + 3 = 0 by taking the square root of both sides.\newlineCalculation: x=−3x = -3

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