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Simplifying 6x2 + 31x = -4 Reorder the terms: 31x + 6x2 = -4 Solving 31x + 6x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + 31x + 6x2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 31x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + 5.166666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 5.166666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 5.166666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 5.166666667x + x2 = 0 + -0.6666666667 5.166666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 5.166666667x + x2 = -0.6666666667 The x term is 5.166666667x. Take half its coefficient (2.583333334). Square it (6.673611115) and add it to both sides. Add '6.673611115' to each side of the equation. 5.166666667x + 6.673611115 + x2 = -0.6666666667 + 6.673611115 Reorder the terms: 6.673611115 + 5.166666667x + x2 = -0.6666666667 + 6.673611115 Combine like terms: -0.6666666667 + 6.673611115 = 6.0069444483 6.673611115 + 5.166666667x + x2 = 6.0069444483 Factor a perfect square on the left side: (x + 2.583333334)(x + 2.583333334) = 6.0069444483 Calculate the square root of the right side: 2.450906862 Break this problem into two subproblems by setting (x + 2.583333334) equal to 2.450906862 and -2.450906862.Subproblem 1
x + 2.583333334 = 2.450906862 Simplifying x + 2.583333334 = 2.450906862 Reorder the terms: 2.583333334 + x = 2.450906862 Solving 2.583333334 + x = 2.450906862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.583333334' to each side of the equation. 2.583333334 + -2.583333334 + x = 2.450906862 + -2.583333334 Combine like terms: 2.583333334 + -2.583333334 = 0.000000000 0.000000000 + x = 2.450906862 + -2.583333334 x = 2.450906862 + -2.583333334 Combine like terms: 2.450906862 + -2.583333334 = -0.132426472 x = -0.132426472 Simplifying x = -0.132426472Subproblem 2
x + 2.583333334 = -2.450906862 Simplifying x + 2.583333334 = -2.450906862 Reorder the terms: 2.583333334 + x = -2.450906862 Solving 2.583333334 + x = -2.450906862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.583333334' to each side of the equation. 2.583333334 + -2.583333334 + x = -2.450906862 + -2.583333334 Combine like terms: 2.583333334 + -2.583333334 = 0.000000000 0.000000000 + x = -2.450906862 + -2.583333334 x = -2.450906862 + -2.583333334 Combine like terms: -2.450906862 + -2.583333334 = -5.034240196 x = -5.034240196 Simplifying x = -5.034240196Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.132426472, -5.034240196}
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