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Simplifying 360x2 + 5x + -36 = 0 Reorder the terms: -36 + 5x + 360x2 = 0 Solving -36 + 5x + 360x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 360 the coefficient of the squared term: Divide each side by '360'. -0.1 + 0.01388888889x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.01388888889x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.01388888889x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.01388888889x + x2 = 0 + 0.1 0.01388888889x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.01388888889x + x2 = 0.1 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 = 0.1 + 0.00004822530865 Reorder the terms: 0.00004822530865 + 0.01388888889x + x2 = 0.1 + 0.00004822530865 Combine like terms: 0.1 + 0.00004822530865 = 0.10004822530865 0.00004822530865 + 0.01388888889x + x2 = 0.10004822530865 Factor a perfect square on the left side: (x + 0.006944444445)(x + 0.006944444445) = 0.10004822530865 Calculate the square root of the right side: 0.316304008 Break this problem into two subproblems by setting (x + 0.006944444445) equal to 0.316304008 and -0.316304008.Subproblem 1
x + 0.006944444445 = 0.316304008 Simplifying x + 0.006944444445 = 0.316304008 Reorder the terms: 0.006944444445 + x = 0.316304008 Solving 0.006944444445 + x = 0.316304008 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 = 0.316304008 + -0.006944444445 Combine like terms: 0.006944444445 + -0.006944444445 = 0.000000000000 0.000000000000 + x = 0.316304008 + -0.006944444445 x = 0.316304008 + -0.006944444445 Combine like terms: 0.316304008 + -0.006944444445 = 0.309359563555 x = 0.309359563555 Simplifying x = 0.309359563555Subproblem 2
x + 0.006944444445 = -0.316304008 Simplifying x + 0.006944444445 = -0.316304008 Reorder the terms: 0.006944444445 + x = -0.316304008 Solving 0.006944444445 + x = -0.316304008 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 = -0.316304008 + -0.006944444445 Combine like terms: 0.006944444445 + -0.006944444445 = 0.000000000000 0.000000000000 + x = -0.316304008 + -0.006944444445 x = -0.316304008 + -0.006944444445 Combine like terms: -0.316304008 + -0.006944444445 = -0.323248452445 x = -0.323248452445 Simplifying x = -0.323248452445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.309359563555, -0.323248452445}
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