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Solve by completing the square. 2k^(2)+12 k+2=0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. k= ◻ or k= ◻

Solve by completing the square.\newline2k2+12k+2=0 2 k^{2}+12 k+2=0 \newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek= k= □ \square or k= k= □ \square \newline

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Q. Solve by completing the square.\newline2k2+12k+2=0 2 k^{2}+12 k+2=0 \newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek= k= □ \square or k= k= □ \square \newline
  1. Divide and Simplify: Step 11: Start by dividing the entire equation by 22 to simplify the coefficients.\newline2k2+12k+2=02k^2 + 12k + 2 = 0 becomes k2+6k+1=0k^2 + 6k + 1 = 0.
  2. Complete the Square: Step 22: To complete the square, calculate (b2)2(\frac{b}{2})^2 where bb is the coefficient of kk. Here, b=6b = 6, so (62)2=9(\frac{6}{2})^2 = 9. Add and subtract 99 inside the equation. k2+6k+9−9+1=0k^2 + 6k + 9 - 9 + 1 = 0 simplifies to (k+3)2−8=0(k + 3)^2 - 8 = 0.
  3. Isolate Perfect Square Term: Step 33: Isolate the perfect square term by moving −8-8 to the right side of the equation.\newline(k+3)2=8(k + 3)^2 = 8.
  4. Take Square Root: Step 44: Take the square root of both sides, remembering to include both the positive and negative roots.\newlinek+3=±8k + 3 = \pm\sqrt{8}.
  5. Simplify Square Root: Step 55: Simplify 8\sqrt{8} to 222\sqrt{2} (since 8=4×2=22\sqrt{8} = \sqrt{4\times2} = 2\sqrt{2}).\newlinek+3=±22.k + 3 = \pm2\sqrt{2}.
  6. Solve for k: Step 66: Solve for k by subtracting 33 from both sides.\newlinek=−3±22.k = -3 \pm 2\sqrt{2}.

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