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Simplifying -14x2 + 3x = -1 Reorder the terms: 3x + -14x2 = -1 Solving 3x + -14x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 3x + -14x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 3x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.07142857143 + -0.2142857143x + x2 = 0 Move the constant term to the right: Add '0.07142857143' to each side of the equation. -0.07142857143 + -0.2142857143x + 0.07142857143 + x2 = 0 + 0.07142857143 Reorder the terms: -0.07142857143 + 0.07142857143 + -0.2142857143x + x2 = 0 + 0.07142857143 Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000 0.00000000000 + -0.2142857143x + x2 = 0 + 0.07142857143 -0.2142857143x + x2 = 0 + 0.07142857143 Combine like terms: 0 + 0.07142857143 = 0.07142857143 -0.2142857143x + x2 = 0.07142857143 The x term is -0.2142857143x. Take half its coefficient (-0.1071428572). Square it (0.01147959185) and add it to both sides. Add '0.01147959185' to each side of the equation. -0.2142857143x + 0.01147959185 + x2 = 0.07142857143 + 0.01147959185 Reorder the terms: 0.01147959185 + -0.2142857143x + x2 = 0.07142857143 + 0.01147959185 Combine like terms: 0.07142857143 + 0.01147959185 = 0.08290816328 0.01147959185 + -0.2142857143x + x2 = 0.08290816328 Factor a perfect square on the left side: (x + -0.1071428572)(x + -0.1071428572) = 0.08290816328 Calculate the square root of the right side: 0.287937777 Break this problem into two subproblems by setting (x + -0.1071428572) equal to 0.287937777 and -0.287937777.Subproblem 1
x + -0.1071428572 = 0.287937777 Simplifying x + -0.1071428572 = 0.287937777 Reorder the terms: -0.1071428572 + x = 0.287937777 Solving -0.1071428572 + x = 0.287937777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1071428572' to each side of the equation. -0.1071428572 + 0.1071428572 + x = 0.287937777 + 0.1071428572 Combine like terms: -0.1071428572 + 0.1071428572 = 0.0000000000 0.0000000000 + x = 0.287937777 + 0.1071428572 x = 0.287937777 + 0.1071428572 Combine like terms: 0.287937777 + 0.1071428572 = 0.3950806342 x = 0.3950806342 Simplifying x = 0.3950806342Subproblem 2
x + -0.1071428572 = -0.287937777 Simplifying x + -0.1071428572 = -0.287937777 Reorder the terms: -0.1071428572 + x = -0.287937777 Solving -0.1071428572 + x = -0.287937777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1071428572' to each side of the equation. -0.1071428572 + 0.1071428572 + x = -0.287937777 + 0.1071428572 Combine like terms: -0.1071428572 + 0.1071428572 = 0.0000000000 0.0000000000 + x = -0.287937777 + 0.1071428572 x = -0.287937777 + 0.1071428572 Combine like terms: -0.287937777 + 0.1071428572 = -0.1807949198 x = -0.1807949198 Simplifying x = -0.1807949198Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3950806342, -0.1807949198}
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