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Simplifying (-6) = 9x2 + 10x + -10 -6 = 9x2 + 10x + -10 Reorder the terms: -6 = -10 + 10x + 9x2 Solving -6 = -10 + 10x + 9x2 Solving for variable 'x'. Combine like terms: -6 + 10 = 4 4 + -10x + -9x2 = -10 + 10x + 9x2 + 10 + -10x + -9x2 Reorder the terms: 4 + -10x + -9x2 = -10 + 10 + 10x + -10x + 9x2 + -9x2 Combine like terms: -10 + 10 = 0 4 + -10x + -9x2 = 0 + 10x + -10x + 9x2 + -9x2 4 + -10x + -9x2 = 10x + -10x + 9x2 + -9x2 Combine like terms: 10x + -10x = 0 4 + -10x + -9x2 = 0 + 9x2 + -9x2 4 + -10x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 4 + -10x + -9x2 = 0 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 = 0.3122499635 x = 0.3122499635 Simplifying x = 0.3122499635Subproblem 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 = -1.4233610745 x = -1.4233610745 Simplifying x = -1.4233610745Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3122499635, -1.4233610745}
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