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Simplifying 36x2 + 5x + -2 = 0 Reorder the terms: -2 + 5x + 36x2 = 0 Solving -2 + 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'. -0.05555555556 + 0.1388888889x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + 0.1388888889x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + 0.1388888889x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + 0.1388888889x + x2 = 0 + 0.05555555556 0.1388888889x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 0.1388888889x + x2 = 0.05555555556 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 = 0.05555555556 + 0.004822530865 Reorder the terms: 0.004822530865 + 0.1388888889x + x2 = 0.05555555556 + 0.004822530865 Combine like terms: 0.05555555556 + 0.004822530865 = 0.060378086425 0.004822530865 + 0.1388888889x + x2 = 0.060378086425 Factor a perfect square on the left side: (x + 0.06944444445)(x + 0.06944444445) = 0.060378086425 Calculate the square root of the right side: 0.245719528 Break this problem into two subproblems by setting (x + 0.06944444445) equal to 0.245719528 and -0.245719528.Subproblem 1
x + 0.06944444445 = 0.245719528 Simplifying x + 0.06944444445 = 0.245719528 Reorder the terms: 0.06944444445 + x = 0.245719528 Solving 0.06944444445 + x = 0.245719528 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 = 0.245719528 + -0.06944444445 Combine like terms: 0.06944444445 + -0.06944444445 = 0.00000000000 0.00000000000 + x = 0.245719528 + -0.06944444445 x = 0.245719528 + -0.06944444445 Combine like terms: 0.245719528 + -0.06944444445 = 0.17627508355 x = 0.17627508355 Simplifying x = 0.17627508355Subproblem 2
x + 0.06944444445 = -0.245719528 Simplifying x + 0.06944444445 = -0.245719528 Reorder the terms: 0.06944444445 + x = -0.245719528 Solving 0.06944444445 + x = -0.245719528 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 = -0.245719528 + -0.06944444445 Combine like terms: 0.06944444445 + -0.06944444445 = 0.00000000000 0.00000000000 + x = -0.245719528 + -0.06944444445 x = -0.245719528 + -0.06944444445 Combine like terms: -0.245719528 + -0.06944444445 = -0.31516397245 x = -0.31516397245 Simplifying x = -0.31516397245Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.17627508355, -0.31516397245}
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