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Simplifying 3x = 1.3x2 + -2x + -270 Reorder the terms: 3x = -270 + -2x + 1.3x2 Solving 3x = -270 + -2x + 1.3x2 Solving for variable 'x'. Reorder the terms: 270 + 3x + 2x + -1.3x2 = -270 + -2x + 1.3x2 + 270 + 2x + -1.3x2 Combine like terms: 3x + 2x = 5x 270 + 5x + -1.3x2 = -270 + -2x + 1.3x2 + 270 + 2x + -1.3x2 Reorder the terms: 270 + 5x + -1.3x2 = -270 + 270 + -2x + 2x + 1.3x2 + -1.3x2 Combine like terms: -270 + 270 = 0 270 + 5x + -1.3x2 = 0 + -2x + 2x + 1.3x2 + -1.3x2 270 + 5x + -1.3x2 = -2x + 2x + 1.3x2 + -1.3x2 Combine like terms: -2x + 2x = 0 270 + 5x + -1.3x2 = 0 + 1.3x2 + -1.3x2 270 + 5x + -1.3x2 = 1.3x2 + -1.3x2 Combine like terms: 1.3x2 + -1.3x2 = 0.0 270 + 5x + -1.3x2 = 0.0 Begin completing the square. Divide all terms by -1.3 the coefficient of the squared term: Divide each side by '-1.3'. -207.6923077 + -3.846153846x + x2 = 0 Move the constant term to the right: Add '207.6923077' to each side of the equation. -207.6923077 + -3.846153846x + 207.6923077 + x2 = 0 + 207.6923077 Reorder the terms: -207.6923077 + 207.6923077 + -3.846153846x + x2 = 0 + 207.6923077 Combine like terms: -207.6923077 + 207.6923077 = 0.0000000 0.0000000 + -3.846153846x + x2 = 0 + 207.6923077 -3.846153846x + x2 = 0 + 207.6923077 Combine like terms: 0 + 207.6923077 = 207.6923077 -3.846153846x + x2 = 207.6923077 The x term is -3.846153846x. Take half its coefficient (-1.923076923). Square it (3.698224852) and add it to both sides. Add '3.698224852' to each side of the equation. -3.846153846x + 3.698224852 + x2 = 207.6923077 + 3.698224852 Reorder the terms: 3.698224852 + -3.846153846x + x2 = 207.6923077 + 3.698224852 Combine like terms: 207.6923077 + 3.698224852 = 211.390532552 3.698224852 + -3.846153846x + x2 = 211.390532552 Factor a perfect square on the left side: (x + -1.923076923)(x + -1.923076923) = 211.390532552 Calculate the square root of the right side: 14.539275517 Break this problem into two subproblems by setting (x + -1.923076923) equal to 14.539275517 and -14.539275517.Subproblem 1
x + -1.923076923 = 14.539275517 Simplifying x + -1.923076923 = 14.539275517 Reorder the terms: -1.923076923 + x = 14.539275517 Solving -1.923076923 + x = 14.539275517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.923076923' to each side of the equation. -1.923076923 + 1.923076923 + x = 14.539275517 + 1.923076923 Combine like terms: -1.923076923 + 1.923076923 = 0.000000000 0.000000000 + x = 14.539275517 + 1.923076923 x = 14.539275517 + 1.923076923 Combine like terms: 14.539275517 + 1.923076923 = 16.46235244 x = 16.46235244 Simplifying x = 16.46235244Subproblem 2
x + -1.923076923 = -14.539275517 Simplifying x + -1.923076923 = -14.539275517 Reorder the terms: -1.923076923 + x = -14.539275517 Solving -1.923076923 + x = -14.539275517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.923076923' to each side of the equation. -1.923076923 + 1.923076923 + x = -14.539275517 + 1.923076923 Combine like terms: -1.923076923 + 1.923076923 = 0.000000000 0.000000000 + x = -14.539275517 + 1.923076923 x = -14.539275517 + 1.923076923 Combine like terms: -14.539275517 + 1.923076923 = -12.616198594 x = -12.616198594 Simplifying x = -12.616198594Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.46235244, -12.616198594}
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