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Simplifying 7x2 + 197x = -3x + 64 + -6x2 Reorder the terms: 197x + 7x2 = -3x + 64 + -6x2 Reorder the terms: 197x + 7x2 = 64 + -3x + -6x2 Solving 197x + 7x2 = 64 + -3x + -6x2 Solving for variable 'x'. Reorder the terms: -64 + 197x + 3x + 7x2 + 6x2 = 64 + -3x + -6x2 + -64 + 3x + 6x2 Combine like terms: 197x + 3x = 200x -64 + 200x + 7x2 + 6x2 = 64 + -3x + -6x2 + -64 + 3x + 6x2 Combine like terms: 7x2 + 6x2 = 13x2 -64 + 200x + 13x2 = 64 + -3x + -6x2 + -64 + 3x + 6x2 Reorder the terms: -64 + 200x + 13x2 = 64 + -64 + -3x + 3x + -6x2 + 6x2 Combine like terms: 64 + -64 = 0 -64 + 200x + 13x2 = 0 + -3x + 3x + -6x2 + 6x2 -64 + 200x + 13x2 = -3x + 3x + -6x2 + 6x2 Combine like terms: -3x + 3x = 0 -64 + 200x + 13x2 = 0 + -6x2 + 6x2 -64 + 200x + 13x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -64 + 200x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -4.923076923 + 15.38461538x + x2 = 0 Move the constant term to the right: Add '4.923076923' to each side of the equation. -4.923076923 + 15.38461538x + 4.923076923 + x2 = 0 + 4.923076923 Reorder the terms: -4.923076923 + 4.923076923 + 15.38461538x + x2 = 0 + 4.923076923 Combine like terms: -4.923076923 + 4.923076923 = 0.000000000 0.000000000 + 15.38461538x + x2 = 0 + 4.923076923 15.38461538x + x2 = 0 + 4.923076923 Combine like terms: 0 + 4.923076923 = 4.923076923 15.38461538x + x2 = 4.923076923 The x term is 15.38461538x. Take half its coefficient (7.69230769). Square it (59.17159760) and add it to both sides. Add '59.17159760' to each side of the equation. 15.38461538x + 59.17159760 + x2 = 4.923076923 + 59.17159760 Reorder the terms: 59.17159760 + 15.38461538x + x2 = 4.923076923 + 59.17159760 Combine like terms: 4.923076923 + 59.17159760 = 64.094674523 59.17159760 + 15.38461538x + x2 = 64.094674523 Factor a perfect square on the left side: (x + 7.69230769)(x + 7.69230769) = 64.094674523 Calculate the square root of the right side: 8.005914971 Break this problem into two subproblems by setting (x + 7.69230769) equal to 8.005914971 and -8.005914971.Subproblem 1
x + 7.69230769 = 8.005914971 Simplifying x + 7.69230769 = 8.005914971 Reorder the terms: 7.69230769 + x = 8.005914971 Solving 7.69230769 + x = 8.005914971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.69230769' to each side of the equation. 7.69230769 + -7.69230769 + x = 8.005914971 + -7.69230769 Combine like terms: 7.69230769 + -7.69230769 = 0.00000000 0.00000000 + x = 8.005914971 + -7.69230769 x = 8.005914971 + -7.69230769 Combine like terms: 8.005914971 + -7.69230769 = 0.313607281 x = 0.313607281 Simplifying x = 0.313607281Subproblem 2
x + 7.69230769 = -8.005914971 Simplifying x + 7.69230769 = -8.005914971 Reorder the terms: 7.69230769 + x = -8.005914971 Solving 7.69230769 + x = -8.005914971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.69230769' to each side of the equation. 7.69230769 + -7.69230769 + x = -8.005914971 + -7.69230769 Combine like terms: 7.69230769 + -7.69230769 = 0.00000000 0.00000000 + x = -8.005914971 + -7.69230769 x = -8.005914971 + -7.69230769 Combine like terms: -8.005914971 + -7.69230769 = -15.698222661 x = -15.698222661 Simplifying x = -15.698222661Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.313607281, -15.698222661}
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