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Simplifying 216x2 + 3x + -14 = 0 Reorder the terms: -14 + 3x + 216x2 = 0 Solving -14 + 3x + 216x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 216 the coefficient of the squared term: Divide each side by '216'. -0.06481481481 + 0.01388888889x + x2 = 0 Move the constant term to the right: Add '0.06481481481' to each side of the equation. -0.06481481481 + 0.01388888889x + 0.06481481481 + x2 = 0 + 0.06481481481 Reorder the terms: -0.06481481481 + 0.06481481481 + 0.01388888889x + x2 = 0 + 0.06481481481 Combine like terms: -0.06481481481 + 0.06481481481 = 0.00000000000 0.00000000000 + 0.01388888889x + x2 = 0 + 0.06481481481 0.01388888889x + x2 = 0 + 0.06481481481 Combine like terms: 0 + 0.06481481481 = 0.06481481481 0.01388888889x + x2 = 0.06481481481 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 = 0.06481481481 + 0.00004822530865 Reorder the terms: 0.00004822530865 + 0.01388888889x + x2 = 0.06481481481 + 0.00004822530865 Combine like terms: 0.06481481481 + 0.00004822530865 = 0.06486304011865 0.00004822530865 + 0.01388888889x + x2 = 0.06486304011865 Factor a perfect square on the left side: (x + 0.006944444445)(x + 0.006944444445) = 0.06486304011865 Calculate the square root of the right side: 0.254682234 Break this problem into two subproblems by setting (x + 0.006944444445) equal to 0.254682234 and -0.254682234.Subproblem 1
x + 0.006944444445 = 0.254682234 Simplifying x + 0.006944444445 = 0.254682234 Reorder the terms: 0.006944444445 + x = 0.254682234 Solving 0.006944444445 + x = 0.254682234 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 = 0.254682234 + -0.006944444445 Combine like terms: 0.006944444445 + -0.006944444445 = 0.000000000000 0.000000000000 + x = 0.254682234 + -0.006944444445 x = 0.254682234 + -0.006944444445 Combine like terms: 0.254682234 + -0.006944444445 = 0.247737789555 x = 0.247737789555 Simplifying x = 0.247737789555Subproblem 2
x + 0.006944444445 = -0.254682234 Simplifying x + 0.006944444445 = -0.254682234 Reorder the terms: 0.006944444445 + x = -0.254682234 Solving 0.006944444445 + x = -0.254682234 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 = -0.254682234 + -0.006944444445 Combine like terms: 0.006944444445 + -0.006944444445 = 0.000000000000 0.000000000000 + x = -0.254682234 + -0.006944444445 x = -0.254682234 + -0.006944444445 Combine like terms: -0.254682234 + -0.006944444445 = -0.261626678445 x = -0.261626678445 Simplifying x = -0.261626678445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.247737789555, -0.261626678445}
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