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Simplifying -17x2 + 13x + 13 = 0 Reorder the terms: 13 + 13x + -17x2 = 0 Solving 13 + 13x + -17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -0.7647058824 + -0.7647058824x + x2 = 0 Move the constant term to the right: Add '0.7647058824' to each side of the equation. -0.7647058824 + -0.7647058824x + 0.7647058824 + x2 = 0 + 0.7647058824 Reorder the terms: -0.7647058824 + 0.7647058824 + -0.7647058824x + x2 = 0 + 0.7647058824 Combine like terms: -0.7647058824 + 0.7647058824 = 0.0000000000 0.0000000000 + -0.7647058824x + x2 = 0 + 0.7647058824 -0.7647058824x + x2 = 0 + 0.7647058824 Combine like terms: 0 + 0.7647058824 = 0.7647058824 -0.7647058824x + x2 = 0.7647058824 The x term is -0.7647058824x. Take half its coefficient (-0.3823529412). Square it (0.1461937716) and add it to both sides. Add '0.1461937716' to each side of the equation. -0.7647058824x + 0.1461937716 + x2 = 0.7647058824 + 0.1461937716 Reorder the terms: 0.1461937716 + -0.7647058824x + x2 = 0.7647058824 + 0.1461937716 Combine like terms: 0.7647058824 + 0.1461937716 = 0.910899654 0.1461937716 + -0.7647058824x + x2 = 0.910899654 Factor a perfect square on the left side: (x + -0.3823529412)(x + -0.3823529412) = 0.910899654 Calculate the square root of the right side: 0.954410632 Break this problem into two subproblems by setting (x + -0.3823529412) equal to 0.954410632 and -0.954410632.Subproblem 1
x + -0.3823529412 = 0.954410632 Simplifying x + -0.3823529412 = 0.954410632 Reorder the terms: -0.3823529412 + x = 0.954410632 Solving -0.3823529412 + x = 0.954410632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3823529412' to each side of the equation. -0.3823529412 + 0.3823529412 + x = 0.954410632 + 0.3823529412 Combine like terms: -0.3823529412 + 0.3823529412 = 0.0000000000 0.0000000000 + x = 0.954410632 + 0.3823529412 x = 0.954410632 + 0.3823529412 Combine like terms: 0.954410632 + 0.3823529412 = 1.3367635732 x = 1.3367635732 Simplifying x = 1.3367635732Subproblem 2
x + -0.3823529412 = -0.954410632 Simplifying x + -0.3823529412 = -0.954410632 Reorder the terms: -0.3823529412 + x = -0.954410632 Solving -0.3823529412 + x = -0.954410632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3823529412' to each side of the equation. -0.3823529412 + 0.3823529412 + x = -0.954410632 + 0.3823529412 Combine like terms: -0.3823529412 + 0.3823529412 = 0.0000000000 0.0000000000 + x = -0.954410632 + 0.3823529412 x = -0.954410632 + 0.3823529412 Combine like terms: -0.954410632 + 0.3823529412 = -0.5720576908 x = -0.5720576908 Simplifying x = -0.5720576908Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3367635732, -0.5720576908}
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