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Simplifying (7x2 + -6x + 29) + (2x2 + 9x + -72) = 0 Reorder the terms: (29 + -6x + 7x2) + (2x2 + 9x + -72) = 0 Remove parenthesis around (29 + -6x + 7x2) 29 + -6x + 7x2 + (2x2 + 9x + -72) = 0 Reorder the terms: 29 + -6x + 7x2 + (-72 + 9x + 2x2) = 0 Remove parenthesis around (-72 + 9x + 2x2) 29 + -6x + 7x2 + -72 + 9x + 2x2 = 0 Reorder the terms: 29 + -72 + -6x + 9x + 7x2 + 2x2 = 0 Combine like terms: 29 + -72 = -43 -43 + -6x + 9x + 7x2 + 2x2 = 0 Combine like terms: -6x + 9x = 3x -43 + 3x + 7x2 + 2x2 = 0 Combine like terms: 7x2 + 2x2 = 9x2 -43 + 3x + 9x2 = 0 Solving -43 + 3x + 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'. -4.777777778 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '4.777777778' to each side of the equation. -4.777777778 + 0.3333333333x + 4.777777778 + x2 = 0 + 4.777777778 Reorder the terms: -4.777777778 + 4.777777778 + 0.3333333333x + x2 = 0 + 4.777777778 Combine like terms: -4.777777778 + 4.777777778 = 0.000000000 0.000000000 + 0.3333333333x + x2 = 0 + 4.777777778 0.3333333333x + x2 = 0 + 4.777777778 Combine like terms: 0 + 4.777777778 = 4.777777778 0.3333333333x + x2 = 4.777777778 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 4.777777778 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 4.777777778 + 0.02777777779 Combine like terms: 4.777777778 + 0.02777777779 = 4.80555555579 0.02777777779 + 0.3333333333x + x2 = 4.80555555579 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 4.80555555579 Calculate the square root of the right side: 2.19215774 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 2.19215774 and -2.19215774.Subproblem 1
x + 0.1666666667 = 2.19215774 Simplifying x + 0.1666666667 = 2.19215774 Reorder the terms: 0.1666666667 + x = 2.19215774 Solving 0.1666666667 + x = 2.19215774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 2.19215774 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 2.19215774 + -0.1666666667 x = 2.19215774 + -0.1666666667 Combine like terms: 2.19215774 + -0.1666666667 = 2.0254910733 x = 2.0254910733 Simplifying x = 2.0254910733Subproblem 2
x + 0.1666666667 = -2.19215774 Simplifying x + 0.1666666667 = -2.19215774 Reorder the terms: 0.1666666667 + x = -2.19215774 Solving 0.1666666667 + x = -2.19215774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -2.19215774 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -2.19215774 + -0.1666666667 x = -2.19215774 + -0.1666666667 Combine like terms: -2.19215774 + -0.1666666667 = -2.3588244067 x = -2.3588244067 Simplifying x = -2.3588244067Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0254910733, -2.3588244067}
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