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Simplifying 6x2 + -17x + 13 = 20x2 + -30 Reorder the terms: 13 + -17x + 6x2 = 20x2 + -30 Reorder the terms: 13 + -17x + 6x2 = -30 + 20x2 Solving 13 + -17x + 6x2 = -30 + 20x2 Solving for variable 'x'. Reorder the terms: 13 + 30 + -17x + 6x2 + -20x2 = -30 + 20x2 + 30 + -20x2 Combine like terms: 13 + 30 = 43 43 + -17x + 6x2 + -20x2 = -30 + 20x2 + 30 + -20x2 Combine like terms: 6x2 + -20x2 = -14x2 43 + -17x + -14x2 = -30 + 20x2 + 30 + -20x2 Reorder the terms: 43 + -17x + -14x2 = -30 + 30 + 20x2 + -20x2 Combine like terms: -30 + 30 = 0 43 + -17x + -14x2 = 0 + 20x2 + -20x2 43 + -17x + -14x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 43 + -17x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -3.071428571 + 1.214285714x + x2 = 0 Move the constant term to the right: Add '3.071428571' to each side of the equation. -3.071428571 + 1.214285714x + 3.071428571 + x2 = 0 + 3.071428571 Reorder the terms: -3.071428571 + 3.071428571 + 1.214285714x + x2 = 0 + 3.071428571 Combine like terms: -3.071428571 + 3.071428571 = 0.000000000 0.000000000 + 1.214285714x + x2 = 0 + 3.071428571 1.214285714x + x2 = 0 + 3.071428571 Combine like terms: 0 + 3.071428571 = 3.071428571 1.214285714x + x2 = 3.071428571 The x term is 1.214285714x. Take half its coefficient (0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. 1.214285714x + 0.3686224488 + x2 = 3.071428571 + 0.3686224488 Reorder the terms: 0.3686224488 + 1.214285714x + x2 = 3.071428571 + 0.3686224488 Combine like terms: 3.071428571 + 0.3686224488 = 3.4400510198 0.3686224488 + 1.214285714x + x2 = 3.4400510198 Factor a perfect square on the left side: (x + 0.607142857)(x + 0.607142857) = 3.4400510198 Calculate the square root of the right side: 1.854737453 Break this problem into two subproblems by setting (x + 0.607142857) equal to 1.854737453 and -1.854737453.Subproblem 1
x + 0.607142857 = 1.854737453 Simplifying x + 0.607142857 = 1.854737453 Reorder the terms: 0.607142857 + x = 1.854737453 Solving 0.607142857 + x = 1.854737453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + x = 1.854737453 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + x = 1.854737453 + -0.607142857 x = 1.854737453 + -0.607142857 Combine like terms: 1.854737453 + -0.607142857 = 1.247594596 x = 1.247594596 Simplifying x = 1.247594596Subproblem 2
x + 0.607142857 = -1.854737453 Simplifying x + 0.607142857 = -1.854737453 Reorder the terms: 0.607142857 + x = -1.854737453 Solving 0.607142857 + x = -1.854737453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + x = -1.854737453 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + x = -1.854737453 + -0.607142857 x = -1.854737453 + -0.607142857 Combine like terms: -1.854737453 + -0.607142857 = -2.46188031 x = -2.46188031 Simplifying x = -2.46188031Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.247594596, -2.46188031}
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