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Simplifying 30x2 + -131x + 70 = 0 Reorder the terms: 70 + -131x + 30x2 = 0 Solving 70 + -131x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 2.333333333 + -4.366666667x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -4.366666667x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -4.366666667x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -4.366666667x + x2 = 0 + -2.333333333 -4.366666667x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -4.366666667x + x2 = -2.333333333 The x term is -4.366666667x. Take half its coefficient (-2.183333334). Square it (4.766944447) and add it to both sides. Add '4.766944447' to each side of the equation. -4.366666667x + 4.766944447 + x2 = -2.333333333 + 4.766944447 Reorder the terms: 4.766944447 + -4.366666667x + x2 = -2.333333333 + 4.766944447 Combine like terms: -2.333333333 + 4.766944447 = 2.433611114 4.766944447 + -4.366666667x + x2 = 2.433611114 Factor a perfect square on the left side: (x + -2.183333334)(x + -2.183333334) = 2.433611114 Calculate the square root of the right side: 1.560003562 Break this problem into two subproblems by setting (x + -2.183333334) equal to 1.560003562 and -1.560003562.Subproblem 1
x + -2.183333334 = 1.560003562 Simplifying x + -2.183333334 = 1.560003562 Reorder the terms: -2.183333334 + x = 1.560003562 Solving -2.183333334 + x = 1.560003562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.183333334' to each side of the equation. -2.183333334 + 2.183333334 + x = 1.560003562 + 2.183333334 Combine like terms: -2.183333334 + 2.183333334 = 0.000000000 0.000000000 + x = 1.560003562 + 2.183333334 x = 1.560003562 + 2.183333334 Combine like terms: 1.560003562 + 2.183333334 = 3.743336896 x = 3.743336896 Simplifying x = 3.743336896Subproblem 2
x + -2.183333334 = -1.560003562 Simplifying x + -2.183333334 = -1.560003562 Reorder the terms: -2.183333334 + x = -1.560003562 Solving -2.183333334 + x = -1.560003562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.183333334' to each side of the equation. -2.183333334 + 2.183333334 + x = -1.560003562 + 2.183333334 Combine like terms: -2.183333334 + 2.183333334 = 0.000000000 0.000000000 + x = -1.560003562 + 2.183333334 x = -1.560003562 + 2.183333334 Combine like terms: -1.560003562 + 2.183333334 = 0.623329772 x = 0.623329772 Simplifying x = 0.623329772Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.743336896, 0.623329772}
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