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Simplifying (3x2 + -3x + -9) + -1(-6x2 + 5x + 7) = 0 Reorder the terms: (-9 + -3x + 3x2) + -1(-6x2 + 5x + 7) = 0 Remove parenthesis around (-9 + -3x + 3x2) -9 + -3x + 3x2 + -1(-6x2 + 5x + 7) = 0 Reorder the terms: -9 + -3x + 3x2 + -1(7 + 5x + -6x2) = 0 -9 + -3x + 3x2 + (7 * -1 + 5x * -1 + -6x2 * -1) = 0 -9 + -3x + 3x2 + (-7 + -5x + 6x2) = 0 Reorder the terms: -9 + -7 + -3x + -5x + 3x2 + 6x2 = 0 Combine like terms: -9 + -7 = -16 -16 + -3x + -5x + 3x2 + 6x2 = 0 Combine like terms: -3x + -5x = -8x -16 + -8x + 3x2 + 6x2 = 0 Combine like terms: 3x2 + 6x2 = 9x2 -16 + -8x + 9x2 = 0 Solving -16 + -8x + 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'. -1.777777778 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -0.8888888889x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -0.8888888889x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -0.8888888889x + x2 = 0 + 1.777777778 -0.8888888889x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -0.8888888889x + x2 = 1.777777778 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 1.777777778 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 1.777777778 + 0.1975308642 Combine like terms: 1.777777778 + 0.1975308642 = 1.9753086422 0.1975308642 + -0.8888888889x + x2 = 1.9753086422 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 1.9753086422 Calculate the square root of the right side: 1.405456738 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 1.405456738 and -1.405456738.Subproblem 1
x + -0.4444444445 = 1.405456738 Simplifying x + -0.4444444445 = 1.405456738 Reorder the terms: -0.4444444445 + x = 1.405456738 Solving -0.4444444445 + x = 1.405456738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 1.405456738 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 1.405456738 + 0.4444444445 x = 1.405456738 + 0.4444444445 Combine like terms: 1.405456738 + 0.4444444445 = 1.8499011825 x = 1.8499011825 Simplifying x = 1.8499011825Subproblem 2
x + -0.4444444445 = -1.405456738 Simplifying x + -0.4444444445 = -1.405456738 Reorder the terms: -0.4444444445 + x = -1.405456738 Solving -0.4444444445 + x = -1.405456738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -1.405456738 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -1.405456738 + 0.4444444445 x = -1.405456738 + 0.4444444445 Combine like terms: -1.405456738 + 0.4444444445 = -0.9610122935 x = -0.9610122935 Simplifying x = -0.9610122935Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8499011825, -0.9610122935}
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