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Solve by completing the square.\newlined2−22d+45=0d^2 - 22d + 45 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlined=d = _____ or d=d = _____

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Solve a quadratic equation by completing the squareright chevron icon

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Q. Solve by completing the square.\newlined2−22d+45=0d^2 - 22d + 45 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlined=d = _____ or d=d = _____
  1. Write Equation Form: Write the equation in the form of d2+bd=cd^2 + bd = c.\newlineSubtract 4545 from both sides to set the equation up for completing the square.\newlined2−22d+45−45=0−45d^2 - 22d + 45 - 45 = 0 - 45\newlined2−22d=−45d^2 - 22d = -45
  2. Subtract to Prepare: Find the number to add to both sides to complete the square.\newlineSince (−222)2=121(-\frac{22}{2})^2 = 121, add 121121 to both sides.\newlined2−22d+121=−45+121d^2 − 22d + 121 = -45 + 121\newlined2−22d+121=76d^2 − 22d + 121 = 76
  3. Find Number to Add: Factor the left side as a perfect square trinomial.\newlined2−22d+121=76d^2 - 22d + 121 = 76\newline(d−11)2=76(d - 11)^2 = 76
  4. Factor Perfect Square: Take the square root of both sides.\newline(d−11)2=±76\sqrt{(d - 11)^2} = \pm\sqrt{76}\newlined−11=±76d - 11 = \pm\sqrt{76}
  5. Take Square Root: Solve for dd by adding 1111 to both sides.\newlined−11+11=±76+11d - 11 + 11 = \pm\sqrt{76} + 11\newlined=11±76d = 11 \pm \sqrt{76}
  6. Solve for dd: Calculate the approximate values of dd.d≈11±8.72d \approx 11 \pm 8.72 (since 76≈8.72\sqrt{76} \approx 8.72)d≈11+8.72d \approx 11 + 8.72 or d≈11−8.72d \approx 11 - 8.72d≈19.72d \approx 19.72 or d≈2.28d \approx 2.28

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