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Simplifying 14x2 + -30x + 1 = 0 Reorder the terms: 1 + -30x + 14x2 = 0 Solving 1 + -30x + 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 + -2.142857143x + x2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + -2.142857143x + -0.07142857143 + x2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + -2.142857143x + x2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + -2.142857143x + x2 = 0 + -0.07142857143 -2.142857143x + x2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 -2.142857143x + x2 = -0.07142857143 The x term is -2.142857143x. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143x + 1.147959185 + x2 = -0.07142857143 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143x + x2 = -0.07142857143 + 1.147959185 Combine like terms: -0.07142857143 + 1.147959185 = 1.07653061357 1.147959185 + -2.142857143x + x2 = 1.07653061357 Factor a perfect square on the left side: (x + -1.071428572)(x + -1.071428572) = 1.07653061357 Calculate the square root of the right side: 1.037559933 Break this problem into two subproblems by setting (x + -1.071428572) equal to 1.037559933 and -1.037559933.Subproblem 1
x + -1.071428572 = 1.037559933 Simplifying x + -1.071428572 = 1.037559933 Reorder the terms: -1.071428572 + x = 1.037559933 Solving -1.071428572 + x = 1.037559933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = 1.037559933 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = 1.037559933 + 1.071428572 x = 1.037559933 + 1.071428572 Combine like terms: 1.037559933 + 1.071428572 = 2.108988505 x = 2.108988505 Simplifying x = 2.108988505Subproblem 2
x + -1.071428572 = -1.037559933 Simplifying x + -1.071428572 = -1.037559933 Reorder the terms: -1.071428572 + x = -1.037559933 Solving -1.071428572 + x = -1.037559933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = -1.037559933 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = -1.037559933 + 1.071428572 x = -1.037559933 + 1.071428572 Combine like terms: -1.037559933 + 1.071428572 = 0.033868639 x = 0.033868639 Simplifying x = 0.033868639Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.108988505, 0.033868639}
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