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Simplifying 17x2 + -13x + -2 = 0 Reorder the terms: -2 + -13x + 17x2 = 0 Solving -2 + -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'. -0.1176470588 + -0.7647058824x + x2 = 0 Move the constant term to the right: Add '0.1176470588' to each side of the equation. -0.1176470588 + -0.7647058824x + 0.1176470588 + x2 = 0 + 0.1176470588 Reorder the terms: -0.1176470588 + 0.1176470588 + -0.7647058824x + x2 = 0 + 0.1176470588 Combine like terms: -0.1176470588 + 0.1176470588 = 0.0000000000 0.0000000000 + -0.7647058824x + x2 = 0 + 0.1176470588 -0.7647058824x + x2 = 0 + 0.1176470588 Combine like terms: 0 + 0.1176470588 = 0.1176470588 -0.7647058824x + x2 = 0.1176470588 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 = 0.1176470588 + 0.1461937716 Reorder the terms: 0.1461937716 + -0.7647058824x + x2 = 0.1176470588 + 0.1461937716 Combine like terms: 0.1176470588 + 0.1461937716 = 0.2638408304 0.1461937716 + -0.7647058824x + x2 = 0.2638408304 Factor a perfect square on the left side: (x + -0.3823529412)(x + -0.3823529412) = 0.2638408304 Calculate the square root of the right side: 0.513654388 Break this problem into two subproblems by setting (x + -0.3823529412) equal to 0.513654388 and -0.513654388.Subproblem 1
x + -0.3823529412 = 0.513654388 Simplifying x + -0.3823529412 = 0.513654388 Reorder the terms: -0.3823529412 + x = 0.513654388 Solving -0.3823529412 + x = 0.513654388 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 = 0.513654388 + 0.3823529412 Combine like terms: -0.3823529412 + 0.3823529412 = 0.0000000000 0.0000000000 + x = 0.513654388 + 0.3823529412 x = 0.513654388 + 0.3823529412 Combine like terms: 0.513654388 + 0.3823529412 = 0.8960073292 x = 0.8960073292 Simplifying x = 0.8960073292Subproblem 2
x + -0.3823529412 = -0.513654388 Simplifying x + -0.3823529412 = -0.513654388 Reorder the terms: -0.3823529412 + x = -0.513654388 Solving -0.3823529412 + x = -0.513654388 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 = -0.513654388 + 0.3823529412 Combine like terms: -0.3823529412 + 0.3823529412 = 0.0000000000 0.0000000000 + x = -0.513654388 + 0.3823529412 x = -0.513654388 + 0.3823529412 Combine like terms: -0.513654388 + 0.3823529412 = -0.1313014468 x = -0.1313014468 Simplifying x = -0.1313014468Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8960073292, -0.1313014468}
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