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Simplifying 3x2 + -49x = 6x2 + -5x + -32 Reorder the terms: -49x + 3x2 = 6x2 + -5x + -32 Reorder the terms: -49x + 3x2 = -32 + -5x + 6x2 Solving -49x + 3x2 = -32 + -5x + 6x2 Solving for variable 'x'. Reorder the terms: 32 + -49x + 5x + 3x2 + -6x2 = -32 + -5x + 6x2 + 32 + 5x + -6x2 Combine like terms: -49x + 5x = -44x 32 + -44x + 3x2 + -6x2 = -32 + -5x + 6x2 + 32 + 5x + -6x2 Combine like terms: 3x2 + -6x2 = -3x2 32 + -44x + -3x2 = -32 + -5x + 6x2 + 32 + 5x + -6x2 Reorder the terms: 32 + -44x + -3x2 = -32 + 32 + -5x + 5x + 6x2 + -6x2 Combine like terms: -32 + 32 = 0 32 + -44x + -3x2 = 0 + -5x + 5x + 6x2 + -6x2 32 + -44x + -3x2 = -5x + 5x + 6x2 + -6x2 Combine like terms: -5x + 5x = 0 32 + -44x + -3x2 = 0 + 6x2 + -6x2 32 + -44x + -3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 32 + -44x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -10.66666667 + 14.66666667x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + 14.66666667x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + 14.66666667x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + 14.66666667x + x2 = 0 + 10.66666667 14.66666667x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 14.66666667x + x2 = 10.66666667 The x term is 14.66666667x. Take half its coefficient (7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. 14.66666667x + 53.77777780 + x2 = 10.66666667 + 53.77777780 Reorder the terms: 53.77777780 + 14.66666667x + x2 = 10.66666667 + 53.77777780 Combine like terms: 10.66666667 + 53.77777780 = 64.44444447 53.77777780 + 14.66666667x + x2 = 64.44444447 Factor a perfect square on the left side: (x + 7.333333335)(x + 7.333333335) = 64.44444447 Calculate the square root of the right side: 8.027729721 Break this problem into two subproblems by setting (x + 7.333333335) equal to 8.027729721 and -8.027729721.Subproblem 1
x + 7.333333335 = 8.027729721 Simplifying x + 7.333333335 = 8.027729721 Reorder the terms: 7.333333335 + x = 8.027729721 Solving 7.333333335 + x = 8.027729721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + x = 8.027729721 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + x = 8.027729721 + -7.333333335 x = 8.027729721 + -7.333333335 Combine like terms: 8.027729721 + -7.333333335 = 0.694396386 x = 0.694396386 Simplifying x = 0.694396386Subproblem 2
x + 7.333333335 = -8.027729721 Simplifying x + 7.333333335 = -8.027729721 Reorder the terms: 7.333333335 + x = -8.027729721 Solving 7.333333335 + x = -8.027729721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + x = -8.027729721 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + x = -8.027729721 + -7.333333335 x = -8.027729721 + -7.333333335 Combine like terms: -8.027729721 + -7.333333335 = -15.361063056 x = -15.361063056 Simplifying x = -15.361063056Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.694396386, -15.361063056}
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