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Simplifying 19x2 + 9x + -14 = 0 Reorder the terms: -14 + 9x + 19x2 = 0 Solving -14 + 9x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.7368421053 + 0.4736842105x + x2 = 0 Move the constant term to the right: Add '0.7368421053' to each side of the equation. -0.7368421053 + 0.4736842105x + 0.7368421053 + x2 = 0 + 0.7368421053 Reorder the terms: -0.7368421053 + 0.7368421053 + 0.4736842105x + x2 = 0 + 0.7368421053 Combine like terms: -0.7368421053 + 0.7368421053 = 0.0000000000 0.0000000000 + 0.4736842105x + x2 = 0 + 0.7368421053 0.4736842105x + x2 = 0 + 0.7368421053 Combine like terms: 0 + 0.7368421053 = 0.7368421053 0.4736842105x + x2 = 0.7368421053 The x term is 0.4736842105x. Take half its coefficient (0.2368421053). Square it (0.05609418284) and add it to both sides. Add '0.05609418284' to each side of the equation. 0.4736842105x + 0.05609418284 + x2 = 0.7368421053 + 0.05609418284 Reorder the terms: 0.05609418284 + 0.4736842105x + x2 = 0.7368421053 + 0.05609418284 Combine like terms: 0.7368421053 + 0.05609418284 = 0.79293628814 0.05609418284 + 0.4736842105x + x2 = 0.79293628814 Factor a perfect square on the left side: (x + 0.2368421053)(x + 0.2368421053) = 0.79293628814 Calculate the square root of the right side: 0.890469701 Break this problem into two subproblems by setting (x + 0.2368421053) equal to 0.890469701 and -0.890469701.Subproblem 1
x + 0.2368421053 = 0.890469701 Simplifying x + 0.2368421053 = 0.890469701 Reorder the terms: 0.2368421053 + x = 0.890469701 Solving 0.2368421053 + x = 0.890469701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2368421053' to each side of the equation. 0.2368421053 + -0.2368421053 + x = 0.890469701 + -0.2368421053 Combine like terms: 0.2368421053 + -0.2368421053 = 0.0000000000 0.0000000000 + x = 0.890469701 + -0.2368421053 x = 0.890469701 + -0.2368421053 Combine like terms: 0.890469701 + -0.2368421053 = 0.6536275957 x = 0.6536275957 Simplifying x = 0.6536275957Subproblem 2
x + 0.2368421053 = -0.890469701 Simplifying x + 0.2368421053 = -0.890469701 Reorder the terms: 0.2368421053 + x = -0.890469701 Solving 0.2368421053 + x = -0.890469701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2368421053' to each side of the equation. 0.2368421053 + -0.2368421053 + x = -0.890469701 + -0.2368421053 Combine like terms: 0.2368421053 + -0.2368421053 = 0.0000000000 0.0000000000 + x = -0.890469701 + -0.2368421053 x = -0.890469701 + -0.2368421053 Combine like terms: -0.890469701 + -0.2368421053 = -1.1273118063 x = -1.1273118063 Simplifying x = -1.1273118063Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6536275957, -1.1273118063}
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