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Simplifying 19x2 + -14x + -1 = 0 Reorder the terms: -1 + -14x + 19x2 = 0 Solving -1 + -14x + 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'. -0.05263157895 + -0.7368421053x + x2 = 0 Move the constant term to the right: Add '0.05263157895' to each side of the equation. -0.05263157895 + -0.7368421053x + 0.05263157895 + x2 = 0 + 0.05263157895 Reorder the terms: -0.05263157895 + 0.05263157895 + -0.7368421053x + x2 = 0 + 0.05263157895 Combine like terms: -0.05263157895 + 0.05263157895 = 0.00000000000 0.00000000000 + -0.7368421053x + x2 = 0 + 0.05263157895 -0.7368421053x + x2 = 0 + 0.05263157895 Combine like terms: 0 + 0.05263157895 = 0.05263157895 -0.7368421053x + x2 = 0.05263157895 The x term is -0.7368421053x. Take half its coefficient (-0.3684210527). Square it (0.1357340721) and add it to both sides. Add '0.1357340721' to each side of the equation. -0.7368421053x + 0.1357340721 + x2 = 0.05263157895 + 0.1357340721 Reorder the terms: 0.1357340721 + -0.7368421053x + x2 = 0.05263157895 + 0.1357340721 Combine like terms: 0.05263157895 + 0.1357340721 = 0.18836565105 0.1357340721 + -0.7368421053x + x2 = 0.18836565105 Factor a perfect square on the left side: (x + -0.3684210527)(x + -0.3684210527) = 0.18836565105 Calculate the square root of the right side: 0.434011119 Break this problem into two subproblems by setting (x + -0.3684210527) equal to 0.434011119 and -0.434011119.Subproblem 1
x + -0.3684210527 = 0.434011119 Simplifying x + -0.3684210527 = 0.434011119 Reorder the terms: -0.3684210527 + x = 0.434011119 Solving -0.3684210527 + x = 0.434011119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3684210527' to each side of the equation. -0.3684210527 + 0.3684210527 + x = 0.434011119 + 0.3684210527 Combine like terms: -0.3684210527 + 0.3684210527 = 0.0000000000 0.0000000000 + x = 0.434011119 + 0.3684210527 x = 0.434011119 + 0.3684210527 Combine like terms: 0.434011119 + 0.3684210527 = 0.8024321717 x = 0.8024321717 Simplifying x = 0.8024321717Subproblem 2
x + -0.3684210527 = -0.434011119 Simplifying x + -0.3684210527 = -0.434011119 Reorder the terms: -0.3684210527 + x = -0.434011119 Solving -0.3684210527 + x = -0.434011119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3684210527' to each side of the equation. -0.3684210527 + 0.3684210527 + x = -0.434011119 + 0.3684210527 Combine like terms: -0.3684210527 + 0.3684210527 = 0.0000000000 0.0000000000 + x = -0.434011119 + 0.3684210527 x = -0.434011119 + 0.3684210527 Combine like terms: -0.434011119 + 0.3684210527 = -0.0655900663 x = -0.0655900663 Simplifying x = -0.0655900663Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8024321717, -0.0655900663}
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