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Simplifying 14x2 + -30x + -3 = 0 Reorder the terms: -3 + -30x + 14x2 = 0 Solving -3 + -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'. -0.2142857143 + -2.142857143x + x2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + -2.142857143x + 0.2142857143 + x2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + -2.142857143x + x2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + -2.142857143x + x2 = 0 + 0.2142857143 -2.142857143x + x2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 -2.142857143x + x2 = 0.2142857143 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 = 0.2142857143 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143x + x2 = 0.2142857143 + 1.147959185 Combine like terms: 0.2142857143 + 1.147959185 = 1.3622448993 1.147959185 + -2.142857143x + x2 = 1.3622448993 Factor a perfect square on the left side: (x + -1.071428572)(x + -1.071428572) = 1.3622448993 Calculate the square root of the right side: 1.167152475 Break this problem into two subproblems by setting (x + -1.071428572) equal to 1.167152475 and -1.167152475.Subproblem 1
x + -1.071428572 = 1.167152475 Simplifying x + -1.071428572 = 1.167152475 Reorder the terms: -1.071428572 + x = 1.167152475 Solving -1.071428572 + x = 1.167152475 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 = 1.167152475 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = 1.167152475 + 1.071428572 x = 1.167152475 + 1.071428572 Combine like terms: 1.167152475 + 1.071428572 = 2.238581047 x = 2.238581047 Simplifying x = 2.238581047Subproblem 2
x + -1.071428572 = -1.167152475 Simplifying x + -1.071428572 = -1.167152475 Reorder the terms: -1.071428572 + x = -1.167152475 Solving -1.071428572 + x = -1.167152475 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 = -1.167152475 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = -1.167152475 + 1.071428572 x = -1.167152475 + 1.071428572 Combine like terms: -1.167152475 + 1.071428572 = -0.095723903 x = -0.095723903 Simplifying x = -0.095723903Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.238581047, -0.095723903}
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