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Simplifying 9x2 + -10x + -5 = 0 Reorder the terms: -5 + -10x + 9x2 = 0 Solving -5 + -10x + 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 + -1.111111111x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -1.111111111x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -1.111111111x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -1.111111111x + x2 = 0 + 0.5555555556 -1.111111111x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -1.111111111x + x2 = 0.5555555556 The x term is -1.111111111x. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111x + 0.3086419752 + x2 = 0.5555555556 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111x + x2 = 0.5555555556 + 0.3086419752 Combine like terms: 0.5555555556 + 0.3086419752 = 0.8641975308 0.3086419752 + -1.111111111x + x2 = 0.8641975308 Factor a perfect square on the left side: (x + -0.5555555555)(x + -0.5555555555) = 0.8641975308 Calculate the square root of the right side: 0.929622252 Break this problem into two subproblems by setting (x + -0.5555555555) equal to 0.929622252 and -0.929622252.Subproblem 1
x + -0.5555555555 = 0.929622252 Simplifying x + -0.5555555555 = 0.929622252 Reorder the terms: -0.5555555555 + x = 0.929622252 Solving -0.5555555555 + x = 0.929622252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = 0.929622252 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = 0.929622252 + 0.5555555555 x = 0.929622252 + 0.5555555555 Combine like terms: 0.929622252 + 0.5555555555 = 1.4851778075 x = 1.4851778075 Simplifying x = 1.4851778075Subproblem 2
x + -0.5555555555 = -0.929622252 Simplifying x + -0.5555555555 = -0.929622252 Reorder the terms: -0.5555555555 + x = -0.929622252 Solving -0.5555555555 + x = -0.929622252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = -0.929622252 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = -0.929622252 + 0.5555555555 x = -0.929622252 + 0.5555555555 Combine like terms: -0.929622252 + 0.5555555555 = -0.3740666965 x = -0.3740666965 Simplifying x = -0.3740666965Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4851778075, -0.3740666965}
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