Solve x^2 + 8x = 10 to complete the square

Answer 1

To solve the equation \( x^2 + 8x = 10 \) by completing the square, follow these steps:

1. Move the constant to the other side: \[ x^2 + 8x - 10 = 0 \]

2. Isolate the \(x^2 + 8x\) term: \[ x^2 + 8x = 10 \]

3. Complete the square:

   • Take the coefficient of \(x\), which is 8, divide it by 2 to get 4, and then square it to get \(16\).
   • Add and subtract \(16\) on the left side: \[ x^2 + 8x + 16 - 16 = 10 \] This simplifies to: \[ (x + 4)^2 - 16 = 10 \]

4. Rearranging gives: \[ (x + 4)^2 = 26 \]

5. Taking the square root of both sides: \[ x + 4 = \pm \sqrt{26} \]

6. Solving for \(x\): \[ x = -4 \pm \sqrt{26} \]

So the solutions are: \[ x = -4 + \sqrt{26} \quad \text{and} \quad x = -4 - \sqrt{26} \]