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Simplifying 14x2 + -17x + -30 = 0 Reorder the terms: -30 + -17x + 14x2 = 0 Solving -30 + -17x + 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'. -2.142857143 + -1.214285714x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + -1.214285714x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + -1.214285714x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + -1.214285714x + x2 = 0 + 2.142857143 -1.214285714x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 -1.214285714x + x2 = 2.142857143 The x term is -1.214285714x. Take half its coefficient (-0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. -1.214285714x + 0.3686224488 + x2 = 2.142857143 + 0.3686224488 Reorder the terms: 0.3686224488 + -1.214285714x + x2 = 2.142857143 + 0.3686224488 Combine like terms: 2.142857143 + 0.3686224488 = 2.5114795918 0.3686224488 + -1.214285714x + x2 = 2.5114795918 Factor a perfect square on the left side: (x + -0.607142857)(x + -0.607142857) = 2.5114795918 Calculate the square root of the right side: 1.584764838 Break this problem into two subproblems by setting (x + -0.607142857) equal to 1.584764838 and -1.584764838.Subproblem 1
x + -0.607142857 = 1.584764838 Simplifying x + -0.607142857 = 1.584764838 Reorder the terms: -0.607142857 + x = 1.584764838 Solving -0.607142857 + x = 1.584764838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.607142857' to each side of the equation. -0.607142857 + 0.607142857 + x = 1.584764838 + 0.607142857 Combine like terms: -0.607142857 + 0.607142857 = 0.000000000 0.000000000 + x = 1.584764838 + 0.607142857 x = 1.584764838 + 0.607142857 Combine like terms: 1.584764838 + 0.607142857 = 2.191907695 x = 2.191907695 Simplifying x = 2.191907695Subproblem 2
x + -0.607142857 = -1.584764838 Simplifying x + -0.607142857 = -1.584764838 Reorder the terms: -0.607142857 + x = -1.584764838 Solving -0.607142857 + x = -1.584764838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.607142857' to each side of the equation. -0.607142857 + 0.607142857 + x = -1.584764838 + 0.607142857 Combine like terms: -0.607142857 + 0.607142857 = 0.000000000 0.000000000 + x = -1.584764838 + 0.607142857 x = -1.584764838 + 0.607142857 Combine like terms: -1.584764838 + 0.607142857 = -0.977621981 x = -0.977621981 Simplifying x = -0.977621981Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.191907695, -0.977621981}
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