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Simplifying (7x2 + -2x + -63) + (6x2 + 4x) = 0 Reorder the terms: (-63 + -2x + 7x2) + (6x2 + 4x) = 0 Remove parenthesis around (-63 + -2x + 7x2) -63 + -2x + 7x2 + (6x2 + 4x) = 0 Reorder the terms: -63 + -2x + 7x2 + (4x + 6x2) = 0 Remove parenthesis around (4x + 6x2) -63 + -2x + 7x2 + 4x + 6x2 = 0 Reorder the terms: -63 + -2x + 4x + 7x2 + 6x2 = 0 Combine like terms: -2x + 4x = 2x -63 + 2x + 7x2 + 6x2 = 0 Combine like terms: 7x2 + 6x2 = 13x2 -63 + 2x + 13x2 = 0 Solving -63 + 2x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -4.846153846 + 0.1538461538x + x2 = 0 Move the constant term to the right: Add '4.846153846' to each side of the equation. -4.846153846 + 0.1538461538x + 4.846153846 + x2 = 0 + 4.846153846 Reorder the terms: -4.846153846 + 4.846153846 + 0.1538461538x + x2 = 0 + 4.846153846 Combine like terms: -4.846153846 + 4.846153846 = 0.000000000 0.000000000 + 0.1538461538x + x2 = 0 + 4.846153846 0.1538461538x + x2 = 0 + 4.846153846 Combine like terms: 0 + 4.846153846 = 4.846153846 0.1538461538x + x2 = 4.846153846 The x term is 0.1538461538x. Take half its coefficient (0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. 0.1538461538x + 0.005917159760 + x2 = 4.846153846 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538x + x2 = 4.846153846 + 0.005917159760 Combine like terms: 4.846153846 + 0.005917159760 = 4.85207100576 0.005917159760 + 0.1538461538x + x2 = 4.85207100576 Factor a perfect square on the left side: (x + 0.0769230769)(x + 0.0769230769) = 4.85207100576 Calculate the square root of the right side: 2.202741702 Break this problem into two subproblems by setting (x + 0.0769230769) equal to 2.202741702 and -2.202741702.Subproblem 1
x + 0.0769230769 = 2.202741702 Simplifying x + 0.0769230769 = 2.202741702 Reorder the terms: 0.0769230769 + x = 2.202741702 Solving 0.0769230769 + x = 2.202741702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = 2.202741702 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = 2.202741702 + -0.0769230769 x = 2.202741702 + -0.0769230769 Combine like terms: 2.202741702 + -0.0769230769 = 2.1258186251 x = 2.1258186251 Simplifying x = 2.1258186251Subproblem 2
x + 0.0769230769 = -2.202741702 Simplifying x + 0.0769230769 = -2.202741702 Reorder the terms: 0.0769230769 + x = -2.202741702 Solving 0.0769230769 + x = -2.202741702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = -2.202741702 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = -2.202741702 + -0.0769230769 x = -2.202741702 + -0.0769230769 Combine like terms: -2.202741702 + -0.0769230769 = -2.2796647789 x = -2.2796647789 Simplifying x = -2.2796647789Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1258186251, -2.2796647789}
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