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Simplifying 9x2 + -3 = 12 + 11x Reorder the terms: -3 + 9x2 = 12 + 11x Solving -3 + 9x2 = 12 + 11x Solving for variable 'x'. Reorder the terms: -3 + -12 + -11x + 9x2 = 12 + 11x + -12 + -11x Combine like terms: -3 + -12 = -15 -15 + -11x + 9x2 = 12 + 11x + -12 + -11x Reorder the terms: -15 + -11x + 9x2 = 12 + -12 + 11x + -11x Combine like terms: 12 + -12 = 0 -15 + -11x + 9x2 = 0 + 11x + -11x -15 + -11x + 9x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -15 + -11x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.666666667 + -1.222222222x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -1.222222222x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -1.222222222x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -1.222222222x + x2 = 0 + 1.666666667 -1.222222222x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -1.222222222x + x2 = 1.666666667 The x term is -1.222222222x. Take half its coefficient (-0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. -1.222222222x + 0.3734567900 + x2 = 1.666666667 + 0.3734567900 Reorder the terms: 0.3734567900 + -1.222222222x + x2 = 1.666666667 + 0.3734567900 Combine like terms: 1.666666667 + 0.3734567900 = 2.040123457 0.3734567900 + -1.222222222x + x2 = 2.040123457 Factor a perfect square on the left side: (x + -0.611111111)(x + -0.611111111) = 2.040123457 Calculate the square root of the right side: 1.428328904 Break this problem into two subproblems by setting (x + -0.611111111) equal to 1.428328904 and -1.428328904.Subproblem 1
x + -0.611111111 = 1.428328904 Simplifying x + -0.611111111 = 1.428328904 Reorder the terms: -0.611111111 + x = 1.428328904 Solving -0.611111111 + x = 1.428328904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + x = 1.428328904 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x = 1.428328904 + 0.611111111 x = 1.428328904 + 0.611111111 Combine like terms: 1.428328904 + 0.611111111 = 2.039440015 x = 2.039440015 Simplifying x = 2.039440015Subproblem 2
x + -0.611111111 = -1.428328904 Simplifying x + -0.611111111 = -1.428328904 Reorder the terms: -0.611111111 + x = -1.428328904 Solving -0.611111111 + x = -1.428328904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + x = -1.428328904 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x = -1.428328904 + 0.611111111 x = -1.428328904 + 0.611111111 Combine like terms: -1.428328904 + 0.611111111 = -0.817217793 x = -0.817217793 Simplifying x = -0.817217793Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.039440015, -0.817217793}
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