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Solve by completing the square.\newlinek2+8k−17=0k^2 + 8k - 17 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____

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Q. Solve by completing the square.\newlinek2+8k−17=0k^2 + 8k - 17 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____
  1. Rewrite Equation: Rewrite the equation in the form of k2+bk=ck^2 + bk = c. We start with the equation k2+8k−17=0k^2 + 8k - 17 = 0 and move the constant term to the right side of the equation. k2+8k=17k^2 + 8k = 17
  2. Complete the Square: Complete the square by adding (b/2)2(b/2)^2 to both sides of the equation.\newlineSince (8/2)2=16(8/2)^2 = 16, we add 1616 to both sides to complete the square.\newlinek2+8k+16=17+16k^2 + 8k + 16 = 17 + 16\newlinek2+8k+16=33k^2 + 8k + 16 = 33
  3. Factor Left Side: Factor the left side of the equation.\newlineThe left side of the equation is now a perfect square trinomial.\newline(k+4)2=33(k + 4)^2 = 33
  4. Take Square Root: Take the square root of both sides of the equation.\newlineWe take the square root of both sides to solve for kk.\newline(k+4)2=±33\sqrt{(k + 4)^2} = \pm\sqrt{33}\newlinek+4=±33k + 4 = \pm\sqrt{33}
  5. Solve for k: Solve for k.\newlineWe isolate k by subtracting 44 from both sides of the equation.\newlinek=−4±33k = -4 \pm \sqrt{33}
  6. Express Solution: Express the solution as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineSince 33\sqrt{33} is an irrational number, we cannot express it as an integer or a fraction. We round it to the nearest hundredth.\newline33≈5.74\sqrt{33} \approx 5.74\newlinek≈−4±5.74k \approx -4 \pm 5.74\newlinek≈−4+5.74k \approx -4 + 5.74 or k≈−4−5.74k \approx -4 - 5.74\newlinek≈1.74k \approx 1.74 or k≈−9.74k \approx -9.74

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