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Simplifying 135x2 + -1x + -45 = 0 Reorder the terms: -45 + -1x + 135x2 = 0 Solving -45 + -1x + 135x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 135 the coefficient of the squared term: Divide each side by '135'. -0.3333333333 + -0.007407407407x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.007407407407x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.007407407407x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.007407407407x + x2 = 0 + 0.3333333333 -0.007407407407x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.007407407407x + x2 = 0.3333333333 The x term is -0.007407407407x. Take half its coefficient (-0.003703703704). Square it (0.00001371742113) and add it to both sides. Add '0.00001371742113' to each side of the equation. -0.007407407407x + 0.00001371742113 + x2 = 0.3333333333 + 0.00001371742113 Reorder the terms: 0.00001371742113 + -0.007407407407x + x2 = 0.3333333333 + 0.00001371742113 Combine like terms: 0.3333333333 + 0.00001371742113 = 0.33334705072113 0.00001371742113 + -0.007407407407x + x2 = 0.33334705072113 Factor a perfect square on the left side: (x + -0.003703703704)(x + -0.003703703704) = 0.33334705072113 Calculate the square root of the right side: 0.577362149 Break this problem into two subproblems by setting (x + -0.003703703704) equal to 0.577362149 and -0.577362149.Subproblem 1
x + -0.003703703704 = 0.577362149 Simplifying x + -0.003703703704 = 0.577362149 Reorder the terms: -0.003703703704 + x = 0.577362149 Solving -0.003703703704 + x = 0.577362149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.003703703704' to each side of the equation. -0.003703703704 + 0.003703703704 + x = 0.577362149 + 0.003703703704 Combine like terms: -0.003703703704 + 0.003703703704 = 0.000000000000 0.000000000000 + x = 0.577362149 + 0.003703703704 x = 0.577362149 + 0.003703703704 Combine like terms: 0.577362149 + 0.003703703704 = 0.581065852704 x = 0.581065852704 Simplifying x = 0.581065852704Subproblem 2
x + -0.003703703704 = -0.577362149 Simplifying x + -0.003703703704 = -0.577362149 Reorder the terms: -0.003703703704 + x = -0.577362149 Solving -0.003703703704 + x = -0.577362149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.003703703704' to each side of the equation. -0.003703703704 + 0.003703703704 + x = -0.577362149 + 0.003703703704 Combine like terms: -0.003703703704 + 0.003703703704 = 0.000000000000 0.000000000000 + x = -0.577362149 + 0.003703703704 x = -0.577362149 + 0.003703703704 Combine like terms: -0.577362149 + 0.003703703704 = -0.573658445296 x = -0.573658445296 Simplifying x = -0.573658445296Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.581065852704, -0.573658445296}
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