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Simplifying 9X2 + -5 + -1X = 0 Reorder the terms: -5 + -1X + 9X2 = 0 Solving -5 + -1X + 9X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + -0.1111111111X + X2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -0.1111111111X + 0.5555555556 + X2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -0.1111111111X + X2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -0.1111111111X + X2 = 0 + 0.5555555556 -0.1111111111X + X2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -0.1111111111X + X2 = 0.5555555556 The X term is -0.1111111111X. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111X + 0.003086419752 + X2 = 0.5555555556 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111X + X2 = 0.5555555556 + 0.003086419752 Combine like terms: 0.5555555556 + 0.003086419752 = 0.558641975352 0.003086419752 + -0.1111111111X + X2 = 0.558641975352 Factor a perfect square on the left side: (X + -0.05555555555)(X + -0.05555555555) = 0.558641975352 Calculate the square root of the right side: 0.747423558 Break this problem into two subproblems by setting (X + -0.05555555555) equal to 0.747423558 and -0.747423558.Subproblem 1
X + -0.05555555555 = 0.747423558 Simplifying X + -0.05555555555 = 0.747423558 Reorder the terms: -0.05555555555 + X = 0.747423558 Solving -0.05555555555 + X = 0.747423558 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + X = 0.747423558 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + X = 0.747423558 + 0.05555555555 X = 0.747423558 + 0.05555555555 Combine like terms: 0.747423558 + 0.05555555555 = 0.80297911355 X = 0.80297911355 Simplifying X = 0.80297911355Subproblem 2
X + -0.05555555555 = -0.747423558 Simplifying X + -0.05555555555 = -0.747423558 Reorder the terms: -0.05555555555 + X = -0.747423558 Solving -0.05555555555 + X = -0.747423558 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + X = -0.747423558 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + X = -0.747423558 + 0.05555555555 X = -0.747423558 + 0.05555555555 Combine like terms: -0.747423558 + 0.05555555555 = -0.69186800245 X = -0.69186800245 Simplifying X = -0.69186800245Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.80297911355, -0.69186800245}
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