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Simplifying 27x2 + -70 = 4x Reorder the terms: -70 + 27x2 = 4x Solving -70 + 27x2 = 4x Solving for variable 'x'. Reorder the terms: -70 + -4x + 27x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -70 + -4x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -2.592592593 + -0.1481481481x + x2 = 0 Move the constant term to the right: Add '2.592592593' to each side of the equation. -2.592592593 + -0.1481481481x + 2.592592593 + x2 = 0 + 2.592592593 Reorder the terms: -2.592592593 + 2.592592593 + -0.1481481481x + x2 = 0 + 2.592592593 Combine like terms: -2.592592593 + 2.592592593 = 0.000000000 0.000000000 + -0.1481481481x + x2 = 0 + 2.592592593 -0.1481481481x + x2 = 0 + 2.592592593 Combine like terms: 0 + 2.592592593 = 2.592592593 -0.1481481481x + x2 = 2.592592593 The x term is -0.1481481481x. Take half its coefficient (-0.07407407405). Square it (0.005486968446) and add it to both sides. Add '0.005486968446' to each side of the equation. -0.1481481481x + 0.005486968446 + x2 = 2.592592593 + 0.005486968446 Reorder the terms: 0.005486968446 + -0.1481481481x + x2 = 2.592592593 + 0.005486968446 Combine like terms: 2.592592593 + 0.005486968446 = 2.598079561446 0.005486968446 + -0.1481481481x + x2 = 2.598079561446 Factor a perfect square on the left side: (x + -0.07407407405)(x + -0.07407407405) = 2.598079561446 Calculate the square root of the right side: 1.611855937 Break this problem into two subproblems by setting (x + -0.07407407405) equal to 1.611855937 and -1.611855937.Subproblem 1
x + -0.07407407405 = 1.611855937 Simplifying x + -0.07407407405 = 1.611855937 Reorder the terms: -0.07407407405 + x = 1.611855937 Solving -0.07407407405 + x = 1.611855937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07407407405' to each side of the equation. -0.07407407405 + 0.07407407405 + x = 1.611855937 + 0.07407407405 Combine like terms: -0.07407407405 + 0.07407407405 = 0.00000000000 0.00000000000 + x = 1.611855937 + 0.07407407405 x = 1.611855937 + 0.07407407405 Combine like terms: 1.611855937 + 0.07407407405 = 1.68593001105 x = 1.68593001105 Simplifying x = 1.68593001105Subproblem 2
x + -0.07407407405 = -1.611855937 Simplifying x + -0.07407407405 = -1.611855937 Reorder the terms: -0.07407407405 + x = -1.611855937 Solving -0.07407407405 + x = -1.611855937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07407407405' to each side of the equation. -0.07407407405 + 0.07407407405 + x = -1.611855937 + 0.07407407405 Combine like terms: -0.07407407405 + 0.07407407405 = 0.00000000000 0.00000000000 + x = -1.611855937 + 0.07407407405 x = -1.611855937 + 0.07407407405 Combine like terms: -1.611855937 + 0.07407407405 = -1.53778186295 x = -1.53778186295 Simplifying x = -1.53778186295Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.68593001105, -1.53778186295}
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