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Simplifying 20x2 + -6x = 6x2 + -13x + 3 Reorder the terms: -6x + 20x2 = 6x2 + -13x + 3 Reorder the terms: -6x + 20x2 = 3 + -13x + 6x2 Solving -6x + 20x2 = 3 + -13x + 6x2 Solving for variable 'x'. Reorder the terms: -3 + -6x + 13x + 20x2 + -6x2 = 3 + -13x + 6x2 + -3 + 13x + -6x2 Combine like terms: -6x + 13x = 7x -3 + 7x + 20x2 + -6x2 = 3 + -13x + 6x2 + -3 + 13x + -6x2 Combine like terms: 20x2 + -6x2 = 14x2 -3 + 7x + 14x2 = 3 + -13x + 6x2 + -3 + 13x + -6x2 Reorder the terms: -3 + 7x + 14x2 = 3 + -3 + -13x + 13x + 6x2 + -6x2 Combine like terms: 3 + -3 = 0 -3 + 7x + 14x2 = 0 + -13x + 13x + 6x2 + -6x2 -3 + 7x + 14x2 = -13x + 13x + 6x2 + -6x2 Combine like terms: -13x + 13x = 0 -3 + 7x + 14x2 = 0 + 6x2 + -6x2 -3 + 7x + 14x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -3 + 7x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2142857143 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.5x + 0.2142857143 + x2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + 0.5x + x2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + 0.2142857143 0.5x + x2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 0.5x + x2 = 0.2142857143 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.2142857143 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.2142857143 + 0.0625 Combine like terms: 0.2142857143 + 0.0625 = 0.2767857143 0.0625 + 0.5x + x2 = 0.2767857143 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.2767857143 Calculate the square root of the right side: 0.526104281 Break this problem into two subproblems by setting (x + 0.25) equal to 0.526104281 and -0.526104281.Subproblem 1
x + 0.25 = 0.526104281 Simplifying x + 0.25 = 0.526104281 Reorder the terms: 0.25 + x = 0.526104281 Solving 0.25 + x = 0.526104281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.526104281 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.526104281 + -0.25 x = 0.526104281 + -0.25 Combine like terms: 0.526104281 + -0.25 = 0.276104281 x = 0.276104281 Simplifying x = 0.276104281Subproblem 2
x + 0.25 = -0.526104281 Simplifying x + 0.25 = -0.526104281 Reorder the terms: 0.25 + x = -0.526104281 Solving 0.25 + x = -0.526104281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.526104281 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.526104281 + -0.25 x = -0.526104281 + -0.25 Combine like terms: -0.526104281 + -0.25 = -0.776104281 x = -0.776104281 Simplifying x = -0.776104281Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.276104281, -0.776104281}
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