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Simplifying 4 + 6x2 + -13x = 0 Reorder the terms: 4 + -13x + 6x2 = 0 Solving 4 + -13x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -2.166666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -2.166666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -2.166666667x + x2 = 0 + -0.6666666667 -2.166666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -2.166666667x + x2 = -0.6666666667 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = -0.6666666667 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = -0.6666666667 + 1.173611113 Combine like terms: -0.6666666667 + 1.173611113 = 0.5069444463 1.173611113 + -2.166666667x + x2 = 0.5069444463 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 0.5069444463 Calculate the square root of the right side: 0.712000313 Break this problem into two subproblems by setting (x + -1.083333334) equal to 0.712000313 and -0.712000313.Subproblem 1
x + -1.083333334 = 0.712000313 Simplifying x + -1.083333334 = 0.712000313 Reorder the terms: -1.083333334 + x = 0.712000313 Solving -1.083333334 + x = 0.712000313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 0.712000313 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 0.712000313 + 1.083333334 x = 0.712000313 + 1.083333334 Combine like terms: 0.712000313 + 1.083333334 = 1.795333647 x = 1.795333647 Simplifying x = 1.795333647Subproblem 2
x + -1.083333334 = -0.712000313 Simplifying x + -1.083333334 = -0.712000313 Reorder the terms: -1.083333334 + x = -0.712000313 Solving -1.083333334 + x = -0.712000313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -0.712000313 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -0.712000313 + 1.083333334 x = -0.712000313 + 1.083333334 Combine like terms: -0.712000313 + 1.083333334 = 0.371333021 x = 0.371333021 Simplifying x = 0.371333021Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.795333647, 0.371333021}
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