X [x + 2 ]= 289 Next Step

General
1

x [X+2 ] =289 Next Step

2

x [x + 2] = 289 Next Step

Answer:
To solve the equation ( x (x + 2) = 289 ), we will follow these steps:

  1. Expand the equation:

    • First, rewrite the given equation in a standard quadratic form.

      x (x + 2) = 289

  2. Simplify the equation:

    • Distribute the ( x ) on the left-hand side.

      x^2 + 2x = 289

  3. Move all terms to one side of the equation:

    • Subtract 289 from both sides of the equation to set it to zero.

      x^2 + 2x - 289 = 0

Now, we have a quadratic equation in the standard form ( ax^2 + bx + c = 0 ), where:

  • ( a = 1 )
  • ( b = 2 )
  • ( c = -289 )

  1. Solve the quadratic equation:

    • We can solve the quadratic equation using the quadratic formula, which is:

      x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

      For our equation, ( a = 1 ), ( b = 2 ), and ( c = -289 ):

      x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-289)}}{2(1)}

  2. Calculate the discriminant:

    • Compute the value under the square root (discriminant).

      b^2 - 4ac = 2^2 - 4(1)(-289) = 4 + 1156 = 1160

  3. Solve for ( x ):

    • Use the discriminant in the quadratic formula.

      x = \frac{-2 \pm \sqrt{1160}}{2}
      • Simplify the expression.
      x = \frac{-2 \pm \sqrt{1160}}{2} = \frac{-2 \pm 34\sqrt{5}}{2}
      x = -1 \pm 17\sqrt{5}

Therefore, the solutions for ( x ) are:

x = -1 + 17\sqrt{5} \quad \text{or} \quad x = -1 - 17\sqrt{5}

Final Answer:
The next step involves expanding, simplifying, and solving the quadratic equation. The solutions are:

x = -1 + 17\sqrt{5} \quad \text{or} \quad x = -1 - 17\sqrt{5}