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Simplifying 36x2 + 2x + -3 = 0 Reorder the terms: -3 + 2x + 36x2 = 0 Solving -3 + 2x + 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'. -0.08333333333 + 0.05555555556x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.05555555556x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.05555555556x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.05555555556x + x2 = 0 + 0.08333333333 0.05555555556x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.05555555556x + x2 = 0.08333333333 The x term is 0.05555555556x. Take half its coefficient (0.02777777778). Square it (0.0007716049384) and add it to both sides. Add '0.0007716049384' to each side of the equation. 0.05555555556x + 0.0007716049384 + x2 = 0.08333333333 + 0.0007716049384 Reorder the terms: 0.0007716049384 + 0.05555555556x + x2 = 0.08333333333 + 0.0007716049384 Combine like terms: 0.08333333333 + 0.0007716049384 = 0.0841049382684 0.0007716049384 + 0.05555555556x + x2 = 0.0841049382684 Factor a perfect square on the left side: (x + 0.02777777778)(x + 0.02777777778) = 0.0841049382684 Calculate the square root of the right side: 0.290008514 Break this problem into two subproblems by setting (x + 0.02777777778) equal to 0.290008514 and -0.290008514.Subproblem 1
x + 0.02777777778 = 0.290008514 Simplifying x + 0.02777777778 = 0.290008514 Reorder the terms: 0.02777777778 + x = 0.290008514 Solving 0.02777777778 + x = 0.290008514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02777777778' to each side of the equation. 0.02777777778 + -0.02777777778 + x = 0.290008514 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = 0.290008514 + -0.02777777778 x = 0.290008514 + -0.02777777778 Combine like terms: 0.290008514 + -0.02777777778 = 0.26223073622 x = 0.26223073622 Simplifying x = 0.26223073622Subproblem 2
x + 0.02777777778 = -0.290008514 Simplifying x + 0.02777777778 = -0.290008514 Reorder the terms: 0.02777777778 + x = -0.290008514 Solving 0.02777777778 + x = -0.290008514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02777777778' to each side of the equation. 0.02777777778 + -0.02777777778 + x = -0.290008514 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = -0.290008514 + -0.02777777778 x = -0.290008514 + -0.02777777778 Combine like terms: -0.290008514 + -0.02777777778 = -0.31778629178 x = -0.31778629178 Simplifying x = -0.31778629178Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.26223073622, -0.31778629178}
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