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Simplifying 9x2 = x + 5 Reorder the terms: 9x2 = 5 + x Solving 9x2 = 5 + x Solving for variable 'x'. Reorder the terms: -5 + -1x + 9x2 = 5 + x + -5 + -1x Reorder the terms: -5 + -1x + 9x2 = 5 + -5 + x + -1x Combine like terms: 5 + -5 = 0 -5 + -1x + 9x2 = 0 + x + -1x -5 + -1x + 9x2 = x + -1x Combine like terms: x + -1x = 0 -5 + -1x + 9x2 = 0 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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