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Simplifying 22d2 + -7d + -5 = 0 Reorder the terms: -5 + -7d + 22d2 = 0 Solving -5 + -7d + 22d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -0.2272727273 + -0.3181818182d + d2 = 0 Move the constant term to the right: Add '0.2272727273' to each side of the equation. -0.2272727273 + -0.3181818182d + 0.2272727273 + d2 = 0 + 0.2272727273 Reorder the terms: -0.2272727273 + 0.2272727273 + -0.3181818182d + d2 = 0 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + -0.3181818182d + d2 = 0 + 0.2272727273 -0.3181818182d + d2 = 0 + 0.2272727273 Combine like terms: 0 + 0.2272727273 = 0.2272727273 -0.3181818182d + d2 = 0.2272727273 The d term is -0.3181818182d. Take half its coefficient (-0.1590909091). Square it (0.02530991736) and add it to both sides. Add '0.02530991736' to each side of the equation. -0.3181818182d + 0.02530991736 + d2 = 0.2272727273 + 0.02530991736 Reorder the terms: 0.02530991736 + -0.3181818182d + d2 = 0.2272727273 + 0.02530991736 Combine like terms: 0.2272727273 + 0.02530991736 = 0.25258264466 0.02530991736 + -0.3181818182d + d2 = 0.25258264466 Factor a perfect square on the left side: (d + -0.1590909091)(d + -0.1590909091) = 0.25258264466 Calculate the square root of the right side: 0.502576009 Break this problem into two subproblems by setting (d + -0.1590909091) equal to 0.502576009 and -0.502576009.Subproblem 1
d + -0.1590909091 = 0.502576009 Simplifying d + -0.1590909091 = 0.502576009 Reorder the terms: -0.1590909091 + d = 0.502576009 Solving -0.1590909091 + d = 0.502576009 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.1590909091' to each side of the equation. -0.1590909091 + 0.1590909091 + d = 0.502576009 + 0.1590909091 Combine like terms: -0.1590909091 + 0.1590909091 = 0.0000000000 0.0000000000 + d = 0.502576009 + 0.1590909091 d = 0.502576009 + 0.1590909091 Combine like terms: 0.502576009 + 0.1590909091 = 0.6616669181 d = 0.6616669181 Simplifying d = 0.6616669181Subproblem 2
d + -0.1590909091 = -0.502576009 Simplifying d + -0.1590909091 = -0.502576009 Reorder the terms: -0.1590909091 + d = -0.502576009 Solving -0.1590909091 + d = -0.502576009 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.1590909091' to each side of the equation. -0.1590909091 + 0.1590909091 + d = -0.502576009 + 0.1590909091 Combine like terms: -0.1590909091 + 0.1590909091 = 0.0000000000 0.0000000000 + d = -0.502576009 + 0.1590909091 d = -0.502576009 + 0.1590909091 Combine like terms: -0.502576009 + 0.1590909091 = -0.3434850999 d = -0.3434850999 Simplifying d = -0.3434850999Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.6616669181, -0.3434850999}
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