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Simplifying 9x2 + 1x + -800 = 0 Reorder the terms: -800 + 1x + 9x2 = 0 Solving -800 + 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'. -88.88888889 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '88.88888889' to each side of the equation. -88.88888889 + 0.1111111111x + 88.88888889 + x2 = 0 + 88.88888889 Reorder the terms: -88.88888889 + 88.88888889 + 0.1111111111x + x2 = 0 + 88.88888889 Combine like terms: -88.88888889 + 88.88888889 = 0.00000000 0.00000000 + 0.1111111111x + x2 = 0 + 88.88888889 0.1111111111x + x2 = 0 + 88.88888889 Combine like terms: 0 + 88.88888889 = 88.88888889 0.1111111111x + x2 = 88.88888889 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 = 88.88888889 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = 88.88888889 + 0.003086419752 Combine like terms: 88.88888889 + 0.003086419752 = 88.891975309752 0.003086419752 + 0.1111111111x + x2 = 88.891975309752 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = 88.891975309752 Calculate the square root of the right side: 9.428254097 Break this problem into two subproblems by setting (x + 0.05555555555) equal to 9.428254097 and -9.428254097.Subproblem 1
x + 0.05555555555 = 9.428254097 Simplifying x + 0.05555555555 = 9.428254097 Reorder the terms: 0.05555555555 + x = 9.428254097 Solving 0.05555555555 + x = 9.428254097 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 = 9.428254097 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 9.428254097 + -0.05555555555 x = 9.428254097 + -0.05555555555 Combine like terms: 9.428254097 + -0.05555555555 = 9.37269854145 x = 9.37269854145 Simplifying x = 9.37269854145Subproblem 2
x + 0.05555555555 = -9.428254097 Simplifying x + 0.05555555555 = -9.428254097 Reorder the terms: 0.05555555555 + x = -9.428254097 Solving 0.05555555555 + x = -9.428254097 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 = -9.428254097 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -9.428254097 + -0.05555555555 x = -9.428254097 + -0.05555555555 Combine like terms: -9.428254097 + -0.05555555555 = -9.48380965255 x = -9.48380965255 Simplifying x = -9.48380965255Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.37269854145, -9.48380965255}
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