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Simplifying 14x2 + 1x + -14 = 0 Reorder the terms: -14 + 1x + 14x2 = 0 Solving -14 + 1x + 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'. -1 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.07142857143x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.07142857143x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.07142857143x + x2 = 0 + 1 0.07142857143x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.07142857143x + x2 = 1 The x term is 0.07142857143x. Take half its coefficient (0.03571428572). Square it (0.001275510204) and add it to both sides. Add '0.001275510204' to each side of the equation. 0.07142857143x + 0.001275510204 + x2 = 1 + 0.001275510204 Reorder the terms: 0.001275510204 + 0.07142857143x + x2 = 1 + 0.001275510204 Combine like terms: 1 + 0.001275510204 = 1.001275510204 0.001275510204 + 0.07142857143x + x2 = 1.001275510204 Factor a perfect square on the left side: (x + 0.03571428572)(x + 0.03571428572) = 1.001275510204 Calculate the square root of the right side: 1.000637552 Break this problem into two subproblems by setting (x + 0.03571428572) equal to 1.000637552 and -1.000637552.Subproblem 1
x + 0.03571428572 = 1.000637552 Simplifying x + 0.03571428572 = 1.000637552 Reorder the terms: 0.03571428572 + x = 1.000637552 Solving 0.03571428572 + x = 1.000637552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = 1.000637552 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = 1.000637552 + -0.03571428572 x = 1.000637552 + -0.03571428572 Combine like terms: 1.000637552 + -0.03571428572 = 0.96492326628 x = 0.96492326628 Simplifying x = 0.96492326628Subproblem 2
x + 0.03571428572 = -1.000637552 Simplifying x + 0.03571428572 = -1.000637552 Reorder the terms: 0.03571428572 + x = -1.000637552 Solving 0.03571428572 + x = -1.000637552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = -1.000637552 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = -1.000637552 + -0.03571428572 x = -1.000637552 + -0.03571428572 Combine like terms: -1.000637552 + -0.03571428572 = -1.03635183772 x = -1.03635183772 Simplifying x = -1.03635183772Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.96492326628, -1.03635183772}
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