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Solve by completing the square.\newlinef2+18f−19=0f^2 + 18f - 19 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = _____ or f=f = _____

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Solve a quadratic equation by completing the squareright chevron icon

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Q. Solve by completing the square.\newlinef2+18f−19=0f^2 + 18f - 19 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = _____ or f=f = _____
  1. Rewrite in standard form: f2+18f−19=0f^2 + 18f - 19 = 0\newlineRewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlineAdd 1919 to both sides.\newlinef2+18f−19+19=0+19f^2 + 18f - 19 + 19 = 0 + 19\newlinef2+18f=19f^2 + 18f = 19
  2. Complete the square: f2+18f=19f^2 + 18f = 19\newlineChoose the equation after completing the square.\newlineSince (182)2=81(\frac{18}{2})^2 = 81, add 8181 to both sides.\newlinef2+18f+81=19+81f^2 + 18f + 81 = 19 + 81\newlinef2+18f+81=100f^2 + 18f + 81 = 100
  3. Factor left side: f2+18f+81=100f^2 + 18f + 81 = 100 Identify the equation after factoring the left side. f2+18f+81=100f^2 + 18f + 81 = 100 (f+182)2=100(f + \frac{18}{2})^2 = 100 (f+9)2=100(f + 9)^2 = 100
  4. Take square root: f+9)2=100(f + 9)^2 = 100(\newlineIdentify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline\$\sqrt{(f + 9)^2} = \sqrt{100}\)\(\newline\)\(f + 9 = \pm\sqrt{100}\)\(\newline\)\(f + 9 = \pm10\)
  5. Isolate variable: We found:\(\newline\)\(f + 9 = \pm10\)\(\newline\)Choose the equation after isolating the variable \(f\).\(\newline\)To isolate \(f\), subtract \(9\) from both sides of the equation.\(\newline\)\(f + 9 - 9 = \pm10 - 9\)\(\newline\)\(f = -9 \pm 10\)
  6. Isolate variable: We found:\(\newline\)\(f + 9 = \pm10\)\(\newline\)Choose the equation after isolating the variable \(f\).\(\newline\)To isolate \(f\), subtract \(9\) from both sides of the equation.\(\newline\)\(f + 9 - 9 = \pm10 - 9\)\(\newline\)\(f = -9 \pm 10\)We have:\(\newline\)\(f = -9 \pm 10\)\(\newline\)What are the two values of \(f\)?\(\newline\)\(f = -9 + 10\) implies \(f = 1\).\(\newline\)\(f\)\(0\) implies \(f\)\(1\).\(\newline\)Values of \(f\): \(f\)\(3\), \(f\)\(4\)

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