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Simplifying 14x2 + -28x + -1 = 0 Reorder the terms: -1 + -28x + 14x2 = 0 Solving -1 + -28x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.07142857143 + -2x + x2 = 0 Move the constant term to the right: Add '0.07142857143' to each side of the equation. -0.07142857143 + -2x + 0.07142857143 + x2 = 0 + 0.07142857143 Reorder the terms: -0.07142857143 + 0.07142857143 + -2x + x2 = 0 + 0.07142857143 Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000 0.00000000000 + -2x + x2 = 0 + 0.07142857143 -2x + x2 = 0 + 0.07142857143 Combine like terms: 0 + 0.07142857143 = 0.07142857143 -2x + x2 = 0.07142857143 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.07142857143 + 1 Reorder the terms: 1 + -2x + x2 = 0.07142857143 + 1 Combine like terms: 0.07142857143 + 1 = 1.07142857143 1 + -2x + x2 = 1.07142857143 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.07142857143 Calculate the square root of the right side: 1.035098339 Break this problem into two subproblems by setting (x + -1) equal to 1.035098339 and -1.035098339.Subproblem 1
x + -1 = 1.035098339 Simplifying x + -1 = 1.035098339 Reorder the terms: -1 + x = 1.035098339 Solving -1 + x = 1.035098339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.035098339 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.035098339 + 1 x = 1.035098339 + 1 Combine like terms: 1.035098339 + 1 = 2.035098339 x = 2.035098339 Simplifying x = 2.035098339Subproblem 2
x + -1 = -1.035098339 Simplifying x + -1 = -1.035098339 Reorder the terms: -1 + x = -1.035098339 Solving -1 + x = -1.035098339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.035098339 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.035098339 + 1 x = -1.035098339 + 1 Combine like terms: -1.035098339 + 1 = -0.035098339 x = -0.035098339 Simplifying x = -0.035098339Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.035098339, -0.035098339}
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