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Solve by completing the square.\newlineg2−16g+25=0g^2 - 16g + 25 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineg=g = _____ or g=g = _____

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Q. Solve by completing the square.\newlineg2−16g+25=0g^2 - 16g + 25 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineg=g = _____ or g=g = _____
  1. Write Equation Form: Write the equation in the form of g2+bg=cg^2 + bg = c. The given equation is already in this form: g2−16g+25=0g^2 - 16g + 25 = 0.
  2. Move Constant Term: Move the constant term to the other side of the equation.\newlineSubtract 2525 from both sides to isolate the gg terms.\newlineg2−16g=−25g^2 - 16g = -25
  3. Complete the Square: Complete the square by adding the square of half the coefficient of gg to both sides.\newlineThe coefficient of gg is −16-16, so half of it is −8-8, and the square of −8-8 is 6464.\newlineAdd 6464 to both sides of the equation.\newlineg2−16g+64=−25+64g^2 − 16g + 64 = -25 + 64\newlineg2−16g+64=39g^2 − 16g + 64 = 39
  4. Factor Left Side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial.\newline(g−8)2=39(g - 8)^2 = 39
  5. Take Square Root: Take the square root of both sides of the equation.\newline(g−8)2=±39\sqrt{(g - 8)^2} = \pm\sqrt{39}\newlineg−8=±39g - 8 = \pm\sqrt{39}
  6. Solve for gg: Solve for gg by isolating the variable.\newlineAdd 88 to both sides of the equation.\newlineg=8±(39)g = 8 \pm \sqrt{(39)}
  7. Calculate Decimal Values: Calculate the approximate decimal values of gg, rounded to the nearest hundredth.39\sqrt{39} is approximately 6.246.24.g≈8+6.24g \approx 8 + 6.24 or g≈8−6.24g \approx 8 - 6.24g≈14.24g \approx 14.24 or g≈1.76g \approx 1.76

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