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Simplifying 6x2 + 13x + -26 = 0 Reorder the terms: -26 + 13x + 6x2 = 0 Solving -26 + 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'. -4.333333333 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + 2.166666667x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + 2.166666667x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + 2.166666667x + x2 = 0 + 4.333333333 2.166666667x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 2.166666667x + x2 = 4.333333333 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 = 4.333333333 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = 4.333333333 + 1.173611113 Combine like terms: 4.333333333 + 1.173611113 = 5.506944446 1.173611113 + 2.166666667x + x2 = 5.506944446 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 5.506944446 Calculate the square root of the right side: 2.346687974 Break this problem into two subproblems by setting (x + 1.083333334) equal to 2.346687974 and -2.346687974.Subproblem 1
x + 1.083333334 = 2.346687974 Simplifying x + 1.083333334 = 2.346687974 Reorder the terms: 1.083333334 + x = 2.346687974 Solving 1.083333334 + x = 2.346687974 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 = 2.346687974 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 2.346687974 + -1.083333334 x = 2.346687974 + -1.083333334 Combine like terms: 2.346687974 + -1.083333334 = 1.26335464 x = 1.26335464 Simplifying x = 1.26335464Subproblem 2
x + 1.083333334 = -2.346687974 Simplifying x + 1.083333334 = -2.346687974 Reorder the terms: 1.083333334 + x = -2.346687974 Solving 1.083333334 + x = -2.346687974 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 = -2.346687974 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -2.346687974 + -1.083333334 x = -2.346687974 + -1.083333334 Combine like terms: -2.346687974 + -1.083333334 = -3.430021308 x = -3.430021308 Simplifying x = -3.430021308Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.26335464, -3.430021308}
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