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Solve by completing the square.\newlinex2−28x−47=0x^2 - 28x - 47 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____

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Q. Solve by completing the square.\newlinex2−28x−47=0x^2 - 28x - 47 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____
  1. Rewrite Equation: Rewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlineAdd 4747 to both sides to set the equation up for completing the square.\newlinex2−28x−47+47=0+47x^2 - 28x - 47 + 47 = 0 + 47\newlinex2−28x=47x^2 - 28x = 47
  2. Add 4747: Choose the number to add to both sides to complete the square.\newlineSince (−282)2=196(-\frac{28}{2})^2 = 196, add 196196 to both sides.\newlinex2−28x+196=47+196x^2 − 28x + 196 = 47 + 196\newlinex2−28x+196=243x^2 − 28x + 196 = 243
  3. Choose Number for Completing Square: Factor the left side of the equation.\newlinex2−28x+196=243x^2 - 28x + 196 = 243\newline(x−14)2=243(x - 14)^2 = 243
  4. Factor Left Side: Take the square root of both sides of the equation.\newline(x−14)2=243\sqrt{(x − 14)^2} = \sqrt{243}\newlinex−14=±243x − 14 = \pm\sqrt{243}
  5. Take Square Root: Solve for xx.\newlineTo isolate xx, add 1414 to both sides of the equation.\newlinex−14+14=±243+14x - 14 + 14 = \pm\sqrt{243} + 14\newlinex=14±243x = 14 \pm \sqrt{243}\newlineSince 243\sqrt{243} is approximately 15.5915.59, we can write:\newlinex≈14±15.59x \approx 14 \pm 15.59
  6. Solve for x: Find the two values of x.\newlinex≈14+15.59x \approx 14 + 15.59 implies x≈29.59x \approx 29.59.\newlinex≈14−15.59x \approx 14 - 15.59 implies x≈−1.59x \approx -1.59.\newlineValues of xx: 29.5929.59, −1.59-1.59

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