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Simplifying 2.6x(x + -2) + 3x = 1.2 Reorder the terms: 2.6x(-2 + x) + 3x = 1.2 (-2 * 2.6x + x * 2.6x) + 3x = 1.2 (-5.2x + 2.6x2) + 3x = 1.2 Reorder the terms: -5.2x + 3x + 2.6x2 = 1.2 Combine like terms: -5.2x + 3x = -2.2x -2.2x + 2.6x2 = 1.2 Solving -2.2x + 2.6x2 = 1.2 Solving for variable 'x'. Reorder the terms: -1.2 + -2.2x + 2.6x2 = 1.2 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 -1.2 + -2.2x + 2.6x2 = 0.0 Begin completing the square. Divide all terms by 2.6 the coefficient of the squared term: Divide each side by '2.6'. -0.4615384615 + -0.8461538462x + x2 = 0 Move the constant term to the right: Add '0.4615384615' to each side of the equation. -0.4615384615 + -0.8461538462x + 0.4615384615 + x2 = 0 + 0.4615384615 Reorder the terms: -0.4615384615 + 0.4615384615 + -0.8461538462x + x2 = 0 + 0.4615384615 Combine like terms: -0.4615384615 + 0.4615384615 = 0.0000000000 0.0000000000 + -0.8461538462x + x2 = 0 + 0.4615384615 -0.8461538462x + x2 = 0 + 0.4615384615 Combine like terms: 0 + 0.4615384615 = 0.4615384615 -0.8461538462x + x2 = 0.4615384615 The x term is -0.8461538462x. Take half its coefficient (-0.4230769231). Square it (0.1789940829) and add it to both sides. Add '0.1789940829' to each side of the equation. -0.8461538462x + 0.1789940829 + x2 = 0.4615384615 + 0.1789940829 Reorder the terms: 0.1789940829 + -0.8461538462x + x2 = 0.4615384615 + 0.1789940829 Combine like terms: 0.4615384615 + 0.1789940829 = 0.6405325444 0.1789940829 + -0.8461538462x + x2 = 0.6405325444 Factor a perfect square on the left side: (x + -0.4230769231)(x + -0.4230769231) = 0.6405325444 Calculate the square root of the right side: 0.800332771 Break this problem into two subproblems by setting (x + -0.4230769231) equal to 0.800332771 and -0.800332771.Subproblem 1
x + -0.4230769231 = 0.800332771 Simplifying x + -0.4230769231 = 0.800332771 Reorder the terms: -0.4230769231 + x = 0.800332771 Solving -0.4230769231 + x = 0.800332771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4230769231' to each side of the equation. -0.4230769231 + 0.4230769231 + x = 0.800332771 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = 0.800332771 + 0.4230769231 x = 0.800332771 + 0.4230769231 Combine like terms: 0.800332771 + 0.4230769231 = 1.2234096941 x = 1.2234096941 Simplifying x = 1.2234096941Subproblem 2
x + -0.4230769231 = -0.800332771 Simplifying x + -0.4230769231 = -0.800332771 Reorder the terms: -0.4230769231 + x = -0.800332771 Solving -0.4230769231 + x = -0.800332771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4230769231' to each side of the equation. -0.4230769231 + 0.4230769231 + x = -0.800332771 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = -0.800332771 + 0.4230769231 x = -0.800332771 + 0.4230769231 Combine like terms: -0.800332771 + 0.4230769231 = -0.3772558479 x = -0.3772558479 Simplifying x = -0.3772558479Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2234096941, -0.3772558479}
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