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Simplifying 36x2 + -5x + -36 = 0 Reorder the terms: -36 + -5x + 36x2 = 0 Solving -36 + -5x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1 + -0.1388888889x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.1388888889x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.1388888889x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.1388888889x + x2 = 0 + 1 -0.1388888889x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.1388888889x + x2 = 1 The x term is -0.1388888889x. Take half its coefficient (-0.06944444445). Square it (0.004822530865) and add it to both sides. Add '0.004822530865' to each side of the equation. -0.1388888889x + 0.004822530865 + x2 = 1 + 0.004822530865 Reorder the terms: 0.004822530865 + -0.1388888889x + x2 = 1 + 0.004822530865 Combine like terms: 1 + 0.004822530865 = 1.004822530865 0.004822530865 + -0.1388888889x + x2 = 1.004822530865 Factor a perfect square on the left side: (x + -0.06944444445)(x + -0.06944444445) = 1.004822530865 Calculate the square root of the right side: 1.002408365 Break this problem into two subproblems by setting (x + -0.06944444445) equal to 1.002408365 and -1.002408365.Subproblem 1
x + -0.06944444445 = 1.002408365 Simplifying x + -0.06944444445 = 1.002408365 Reorder the terms: -0.06944444445 + x = 1.002408365 Solving -0.06944444445 + x = 1.002408365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06944444445' to each side of the equation. -0.06944444445 + 0.06944444445 + x = 1.002408365 + 0.06944444445 Combine like terms: -0.06944444445 + 0.06944444445 = 0.00000000000 0.00000000000 + x = 1.002408365 + 0.06944444445 x = 1.002408365 + 0.06944444445 Combine like terms: 1.002408365 + 0.06944444445 = 1.07185280945 x = 1.07185280945 Simplifying x = 1.07185280945Subproblem 2
x + -0.06944444445 = -1.002408365 Simplifying x + -0.06944444445 = -1.002408365 Reorder the terms: -0.06944444445 + x = -1.002408365 Solving -0.06944444445 + x = -1.002408365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06944444445' to each side of the equation. -0.06944444445 + 0.06944444445 + x = -1.002408365 + 0.06944444445 Combine like terms: -0.06944444445 + 0.06944444445 = 0.00000000000 0.00000000000 + x = -1.002408365 + 0.06944444445 x = -1.002408365 + 0.06944444445 Combine like terms: -1.002408365 + 0.06944444445 = -0.93296392055 x = -0.93296392055 Simplifying x = -0.93296392055Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.07185280945, -0.93296392055}
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