Question

X² + 10x + 17 =0

Solve by completing the sqaure

Answer 1

Answers:
`\text{x} = 5+2√(2) \ \ \text{ or } \ \ \text{x} = 5-2√(2)`

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Step-by-step explanation:

The x coefficient is 10, which divides in half to get 5.

Square this to get 5^2 = 5*5 = 25

We need to add 25 to both sides so that the x² + 10x portion gets to x² + 10x+25 and we can factor it to (x+5)²

Here's what the steps look like when we complete the square.

`\text{x}^2 + 10\text{x} + 17 =0\\\\\text{x}^2 + 10\text{x} + 17+25 =0+25\\\\(\text{x}^2 + 10\text{x}+25) + 17 = 25\\\\(\text{x}+5)^2+17 = 25\\\\(\text{x}+5)^2 = 25-17\\\\(\text{x}+5)^2 = 8\\\\`

Then we apply the square root to both sides. Don't forget about the plus/minus.

`(\text{x}+5)^2 = 8\\\\\sqrt{(\text{x}+5)^2} = √(8)\\\\|\text{x}+5| = √(8)\\\\\text{x}+5 = \pm√(8)\\\\\text{x}+5 = \pm2√(2)\\\\\text{x} = 5\pm2√(2)\\\\\text{x} = 5+2√(2) \ \ \text{ or } \ \ \text{x} = 5+2√(2)\\\\`

You can use the quadratic formula to verify the two roots.