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Simplifying 9x2 + -10x + -4 = 0 Reorder the terms: -4 + -10x + 9x2 = 0 Solving -4 + -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'. -0.4444444444 + -1.111111111x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -1.111111111x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -1.111111111x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -1.111111111x + x2 = 0 + 0.4444444444 -1.111111111x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -1.111111111x + x2 = 0.4444444444 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 = 0.4444444444 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111x + x2 = 0.4444444444 + 0.3086419752 Combine like terms: 0.4444444444 + 0.3086419752 = 0.7530864196 0.3086419752 + -1.111111111x + x2 = 0.7530864196 Factor a perfect square on the left side: (x + -0.5555555555)(x + -0.5555555555) = 0.7530864196 Calculate the square root of the right side: 0.867805519 Break this problem into two subproblems by setting (x + -0.5555555555) equal to 0.867805519 and -0.867805519.Subproblem 1
x + -0.5555555555 = 0.867805519 Simplifying x + -0.5555555555 = 0.867805519 Reorder the terms: -0.5555555555 + x = 0.867805519 Solving -0.5555555555 + x = 0.867805519 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 = 0.867805519 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = 0.867805519 + 0.5555555555 x = 0.867805519 + 0.5555555555 Combine like terms: 0.867805519 + 0.5555555555 = 1.4233610745 x = 1.4233610745 Simplifying x = 1.4233610745Subproblem 2
x + -0.5555555555 = -0.867805519 Simplifying x + -0.5555555555 = -0.867805519 Reorder the terms: -0.5555555555 + x = -0.867805519 Solving -0.5555555555 + x = -0.867805519 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 = -0.867805519 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = -0.867805519 + 0.5555555555 x = -0.867805519 + 0.5555555555 Combine like terms: -0.867805519 + 0.5555555555 = -0.3122499635 x = -0.3122499635 Simplifying x = -0.3122499635Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4233610745, -0.3122499635}
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