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Simplifying 9x2 + -3 = -10x Reorder the terms: -3 + 9x2 = -10x Solving -3 + 9x2 = -10x Solving for variable 'x'. Reorder the terms: -3 + 10x + 9x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -3 + 10x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + 1.111111111x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.111111111x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.111111111x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.111111111x + x2 = 0 + 0.3333333333 1.111111111x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.111111111x + x2 = 0.3333333333 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 = 0.3333333333 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x + x2 = 0.3333333333 + 0.3086419752 Combine like terms: 0.3333333333 + 0.3086419752 = 0.6419753085 0.3086419752 + 1.111111111x + x2 = 0.6419753085 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 0.6419753085 Calculate the square root of the right side: 0.801233617 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 0.801233617 and -0.801233617.Subproblem 1
x + 0.5555555555 = 0.801233617 Simplifying x + 0.5555555555 = 0.801233617 Reorder the terms: 0.5555555555 + x = 0.801233617 Solving 0.5555555555 + x = 0.801233617 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 = 0.801233617 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 0.801233617 + -0.5555555555 x = 0.801233617 + -0.5555555555 Combine like terms: 0.801233617 + -0.5555555555 = 0.2456780615 x = 0.2456780615 Simplifying x = 0.2456780615Subproblem 2
x + 0.5555555555 = -0.801233617 Simplifying x + 0.5555555555 = -0.801233617 Reorder the terms: 0.5555555555 + x = -0.801233617 Solving 0.5555555555 + x = -0.801233617 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 = -0.801233617 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -0.801233617 + -0.5555555555 x = -0.801233617 + -0.5555555555 Combine like terms: -0.801233617 + -0.5555555555 = -1.3567891725 x = -1.3567891725 Simplifying x = -1.3567891725Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2456780615, -1.3567891725}
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