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Simplifying 72x2 + -1x + -10 = 0 Reorder the terms: -10 + -1x + 72x2 = 0 Solving -10 + -1x + 72x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. -0.1388888889 + -0.01388888889x + x2 = 0 Move the constant term to the right: Add '0.1388888889' to each side of the equation. -0.1388888889 + -0.01388888889x + 0.1388888889 + x2 = 0 + 0.1388888889 Reorder the terms: -0.1388888889 + 0.1388888889 + -0.01388888889x + x2 = 0 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + -0.01388888889x + x2 = 0 + 0.1388888889 -0.01388888889x + x2 = 0 + 0.1388888889 Combine like terms: 0 + 0.1388888889 = 0.1388888889 -0.01388888889x + x2 = 0.1388888889 The x term is -0.01388888889x. Take half its coefficient (-0.006944444445). Square it (0.00004822530865) and add it to both sides. Add '0.00004822530865' to each side of the equation. -0.01388888889x + 0.00004822530865 + x2 = 0.1388888889 + 0.00004822530865 Reorder the terms: 0.00004822530865 + -0.01388888889x + x2 = 0.1388888889 + 0.00004822530865 Combine like terms: 0.1388888889 + 0.00004822530865 = 0.13893711420865 0.00004822530865 + -0.01388888889x + x2 = 0.13893711420865 Factor a perfect square on the left side: (x + -0.006944444445)(x + -0.006944444445) = 0.13893711420865 Calculate the square root of the right side: 0.372742692 Break this problem into two subproblems by setting (x + -0.006944444445) equal to 0.372742692 and -0.372742692.Subproblem 1
x + -0.006944444445 = 0.372742692 Simplifying x + -0.006944444445 = 0.372742692 Reorder the terms: -0.006944444445 + x = 0.372742692 Solving -0.006944444445 + x = 0.372742692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006944444445' to each side of the equation. -0.006944444445 + 0.006944444445 + x = 0.372742692 + 0.006944444445 Combine like terms: -0.006944444445 + 0.006944444445 = 0.000000000000 0.000000000000 + x = 0.372742692 + 0.006944444445 x = 0.372742692 + 0.006944444445 Combine like terms: 0.372742692 + 0.006944444445 = 0.379687136445 x = 0.379687136445 Simplifying x = 0.379687136445Subproblem 2
x + -0.006944444445 = -0.372742692 Simplifying x + -0.006944444445 = -0.372742692 Reorder the terms: -0.006944444445 + x = -0.372742692 Solving -0.006944444445 + x = -0.372742692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006944444445' to each side of the equation. -0.006944444445 + 0.006944444445 + x = -0.372742692 + 0.006944444445 Combine like terms: -0.006944444445 + 0.006944444445 = 0.000000000000 0.000000000000 + x = -0.372742692 + 0.006944444445 x = -0.372742692 + 0.006944444445 Combine like terms: -0.372742692 + 0.006944444445 = -0.365798247555 x = -0.365798247555 Simplifying x = -0.365798247555Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.379687136445, -0.365798247555}
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