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Simplifying 3x2 + -2x = 13x + 20 Reorder the terms: -2x + 3x2 = 13x + 20 Reorder the terms: -2x + 3x2 = 20 + 13x Solving -2x + 3x2 = 20 + 13x Solving for variable 'x'. Reorder the terms: -20 + -2x + -13x + 3x2 = 20 + 13x + -20 + -13x Combine like terms: -2x + -13x = -15x -20 + -15x + 3x2 = 20 + 13x + -20 + -13x Reorder the terms: -20 + -15x + 3x2 = 20 + -20 + 13x + -13x Combine like terms: 20 + -20 = 0 -20 + -15x + 3x2 = 0 + 13x + -13x -20 + -15x + 3x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -20 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.666666667 + -5x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -5x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -5x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -5x + x2 = 0 + 6.666666667 -5x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -5x + x2 = 6.666666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 6.666666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 6.666666667 + 6.25 Combine like terms: 6.666666667 + 6.25 = 12.916666667 6.25 + -5x + x2 = 12.916666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 12.916666667 Calculate the square root of the right side: 3.593976442 Break this problem into two subproblems by setting (x + -2.5) equal to 3.593976442 and -3.593976442.Subproblem 1
x + -2.5 = 3.593976442 Simplifying x + -2.5 = 3.593976442 Reorder the terms: -2.5 + x = 3.593976442 Solving -2.5 + x = 3.593976442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.593976442 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.593976442 + 2.5 x = 3.593976442 + 2.5 Combine like terms: 3.593976442 + 2.5 = 6.093976442 x = 6.093976442 Simplifying x = 6.093976442Subproblem 2
x + -2.5 = -3.593976442 Simplifying x + -2.5 = -3.593976442 Reorder the terms: -2.5 + x = -3.593976442 Solving -2.5 + x = -3.593976442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.593976442 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.593976442 + 2.5 x = -3.593976442 + 2.5 Combine like terms: -3.593976442 + 2.5 = -1.093976442 x = -1.093976442 Simplifying x = -1.093976442Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.093976442, -1.093976442}
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