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Solve by completing the square.\newlineg2+2g=47g^2 + 2g = 47\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+2g=47g^2 + 2g = 47\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+2g=47g^2 + 2g = 47.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlineSubtract 4747 from both sides to isolate the gg terms.\newlineg2+2g−47=0g^2 + 2g - 47 = 0\newlineg2+2g=47g^2 + 2g = 47
  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 22, so half of it is 11. The square of 11 is 11.\newlineAdd 11 to both sides of the equation.\newlineg2+2g+1=47+1g^2 + 2g + 1 = 47 + 1\newlineg2+2g+1=48g^2 + 2g + 1 = 48
  4. Factor Left Side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial.\newline(g+1)2=48(g + 1)^2 = 48
  5. Take Square Root: Take the square root of both sides of the equation.\newline(g+1)2=±48\sqrt{(g + 1)^2} = \pm\sqrt{48}\newlineg+1=±48g + 1 = \pm\sqrt{48}
  6. Simplify Square Root: Simplify the square root of 4848.48\sqrt{48} can be simplified to 16×3\sqrt{16 \times 3} which is 434\sqrt{3}.g+1=±43g + 1 = \pm 4\sqrt{3}
  7. Isolate Variable: Isolate gg by subtracting 11 from both sides.\newlineg=−1±43g = -1 \pm 4\sqrt{3}
  8. Calculate Approximate Values: Calculate the approximate decimal values of gg.434\sqrt{3} is approximately 6.936.93 (rounded to the nearest hundredth).g≈−1+6.93g \approx -1 + 6.93 or g≈−1−6.93g \approx -1 - 6.93g≈5.93g \approx 5.93 or g≈−7.93g \approx -7.93

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