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Solve by completing the square.\newlined2+6d−7=0d^2 + 6d - 7 = 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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Q. Solve by completing the square.\newlined2+6d−7=0d^2 + 6d - 7 = 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. Rewrite and Add Constant: d2+6d−7=0d^2 + 6d - 7 = 0\newlineRewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlineAdd 77 to both sides to move the constant term to the right side of the equation.\newlined2+6d−7+7=0+7d^2 + 6d - 7 + 7 = 0 + 7\newlined2+6d=7d^2 + 6d = 7
  2. Complete the Square: d2+6d=7d^2 + 6d = 7\newlineChoose the equation after completing the square.\newlineSince (6/2)2=9(6/2)^2 = 9, add 99 to both sides to complete the square.\newlined2+6d+9=7+9d^2 + 6d + 9 = 7 + 9\newlined2+6d+9=16d^2 + 6d + 9 = 16
  3. Identify Factored Equation: d2+6d+9=16d^2 + 6d + 9 = 16\newlineIdentify the equation after factoring the left side.\newline(d+3)2=16(d + 3)^2 = 16
  4. Take Square Root: d+3)2=16(d + 3)^2 = 16(\newlineIdentify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline\$\sqrt{(d + 3)^2} = \sqrt{16}\)\(\newline\)\(d + 3 = \pm 4\)
  5. Isolate Variable: We found:\(\newline\)\(d + 3 = \pm4\)\(\newline\)Choose the equation after isolating the variable \(d\).\(\newline\)To isolate \(d\), subtract \(3\) from both sides of the equation.\(\newline\)\(d + 3 - 3 = \pm4 - 3\)\(\newline\)\(d = \pm4 - 3\)
  6. Find Values of d: We have:\(\newline\)d = \(\pm 4 - 3\)\(\newline\)What are the two values of d?\(\newline\)d = \(4 - 3\) implies d = \(1\).\(\newline\)d = \(-4 - 3\) implies d = \(-7\).\(\newline\)Values of d: \(1\), \(-7\)

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