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Simplifying -2 + -13.8x = -8x(6x + 1) Reorder the terms: -2 + -13.8x = -8x(1 + 6x) -2 + -13.8x = (1 * -8x + 6x * -8x) -2 + -13.8x = (-8x + -48x2) Solving -2 + -13.8x = -8x + -48x2 Solving for variable 'x'. Combine like terms: -13.8x + 8x = -5.8x -2 + -5.8x + 48x2 = -8x + -48x2 + 8x + 48x2 Reorder the terms: -2 + -5.8x + 48x2 = -8x + 8x + -48x2 + 48x2 Combine like terms: -8x + 8x = 0 -2 + -5.8x + 48x2 = 0 + -48x2 + 48x2 -2 + -5.8x + 48x2 = -48x2 + 48x2 Combine like terms: -48x2 + 48x2 = 0 -2 + -5.8x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.04166666667 + -0.1208333333x + x2 = 0 Move the constant term to the right: Add '0.04166666667' to each side of the equation. -0.04166666667 + -0.1208333333x + 0.04166666667 + x2 = 0 + 0.04166666667 Reorder the terms: -0.04166666667 + 0.04166666667 + -0.1208333333x + x2 = 0 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + -0.1208333333x + x2 = 0 + 0.04166666667 -0.1208333333x + x2 = 0 + 0.04166666667 Combine like terms: 0 + 0.04166666667 = 0.04166666667 -0.1208333333x + x2 = 0.04166666667 The x term is -0.1208333333x. Take half its coefficient (-0.06041666665). Square it (0.003650173609) and add it to both sides. Add '0.003650173609' to each side of the equation. -0.1208333333x + 0.003650173609 + x2 = 0.04166666667 + 0.003650173609 Reorder the terms: 0.003650173609 + -0.1208333333x + x2 = 0.04166666667 + 0.003650173609 Combine like terms: 0.04166666667 + 0.003650173609 = 0.045316840279 0.003650173609 + -0.1208333333x + x2 = 0.045316840279 Factor a perfect square on the left side: (x + -0.06041666665)(x + -0.06041666665) = 0.045316840279 Calculate the square root of the right side: 0.212877524 Break this problem into two subproblems by setting (x + -0.06041666665) equal to 0.212877524 and -0.212877524.Subproblem 1
x + -0.06041666665 = 0.212877524 Simplifying x + -0.06041666665 = 0.212877524 Reorder the terms: -0.06041666665 + x = 0.212877524 Solving -0.06041666665 + x = 0.212877524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06041666665' to each side of the equation. -0.06041666665 + 0.06041666665 + x = 0.212877524 + 0.06041666665 Combine like terms: -0.06041666665 + 0.06041666665 = 0.00000000000 0.00000000000 + x = 0.212877524 + 0.06041666665 x = 0.212877524 + 0.06041666665 Combine like terms: 0.212877524 + 0.06041666665 = 0.27329419065 x = 0.27329419065 Simplifying x = 0.27329419065Subproblem 2
x + -0.06041666665 = -0.212877524 Simplifying x + -0.06041666665 = -0.212877524 Reorder the terms: -0.06041666665 + x = -0.212877524 Solving -0.06041666665 + x = -0.212877524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06041666665' to each side of the equation. -0.06041666665 + 0.06041666665 + x = -0.212877524 + 0.06041666665 Combine like terms: -0.06041666665 + 0.06041666665 = 0.00000000000 0.00000000000 + x = -0.212877524 + 0.06041666665 x = -0.212877524 + 0.06041666665 Combine like terms: -0.212877524 + 0.06041666665 = -0.15246085735 x = -0.15246085735 Simplifying x = -0.15246085735Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.27329419065, -0.15246085735}
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