Questions: Solve for x. x^2 + 9x + 18 = 0

Solve for x. x^2 + 9x + 18 = 0

Solution

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Solution Steps

To solve the quadratic equation \(x^2 + 9x + 18 = 0\), we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a\), \(b\), and \(c\) are the coefficients of the equation \(ax^2 + bx + c = 0\).

Step 1: Identify Coefficients

The given quadratic equation is \(x^2 + 9x + 18 = 0\). Here, the coefficients are:

  • \(a = 1\)
  • \(b = 9\)
  • \(c = 18\)
Step 2: Calculate the Discriminant

The discriminant \(D\) is calculated using the formula: \[ D = b^2 - 4ac \] Substituting the values: \[ D = 9^2 - 4 \cdot 1 \cdot 18 = 81 - 72 = 9 \]

Step 3: Apply the Quadratic Formula

Using the quadratic formula: \[ x = \frac{-b \pm \sqrt{D}}{2a} \] Substituting the values: \[ x = \frac{-9 \pm \sqrt{9}}{2 \cdot 1} = \frac{-9 \pm 3}{2} \]

Step 4: Calculate the Roots

Calculating the two possible values for \(x\):

  1. For \(x_1\): \[ x_1 = \frac{-9 + 3}{2} = \frac{-6}{2} = -3.0 \]
  2. For \(x_2\): \[ x_2 = \frac{-9 - 3}{2} = \frac{-12}{2} = -6.0 \]

Final Answer

The solutions to the equation are: \[ \boxed{x_1 = -3.0} \] \[ \boxed{x_2 = -6.0} \]

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