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Simplifying (3x + -50)(2x + -5) = 180 Reorder the terms: (-50 + 3x)(2x + -5) = 180 Reorder the terms: (-50 + 3x)(-5 + 2x) = 180 Multiply (-50 + 3x) * (-5 + 2x) (-50(-5 + 2x) + 3x * (-5 + 2x)) = 180 ((-5 * -50 + 2x * -50) + 3x * (-5 + 2x)) = 180 ((250 + -100x) + 3x * (-5 + 2x)) = 180 (250 + -100x + (-5 * 3x + 2x * 3x)) = 180 (250 + -100x + (-15x + 6x2)) = 180 Combine like terms: -100x + -15x = -115x (250 + -115x + 6x2) = 180 Solving 250 + -115x + 6x2 = 180 Solving for variable 'x'. Reorder the terms: 250 + -180 + -115x + 6x2 = 180 + -180 Combine like terms: 250 + -180 = 70 70 + -115x + 6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 70 + -115x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 11.66666667 + -19.16666667x + x2 = 0 Move the constant term to the right: Add '-11.66666667' to each side of the equation. 11.66666667 + -19.16666667x + -11.66666667 + x2 = 0 + -11.66666667 Reorder the terms: 11.66666667 + -11.66666667 + -19.16666667x + x2 = 0 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + -19.16666667x + x2 = 0 + -11.66666667 -19.16666667x + x2 = 0 + -11.66666667 Combine like terms: 0 + -11.66666667 = -11.66666667 -19.16666667x + x2 = -11.66666667 The x term is -19.16666667x. Take half its coefficient (-9.583333335). Square it (91.84027781) and add it to both sides. Add '91.84027781' to each side of the equation. -19.16666667x + 91.84027781 + x2 = -11.66666667 + 91.84027781 Reorder the terms: 91.84027781 + -19.16666667x + x2 = -11.66666667 + 91.84027781 Combine like terms: -11.66666667 + 91.84027781 = 80.17361114 91.84027781 + -19.16666667x + x2 = 80.17361114 Factor a perfect square on the left side: (x + -9.583333335)(x + -9.583333335) = 80.17361114 Calculate the square root of the right side: 8.953971808 Break this problem into two subproblems by setting (x + -9.583333335) equal to 8.953971808 and -8.953971808.Subproblem 1
x + -9.583333335 = 8.953971808 Simplifying x + -9.583333335 = 8.953971808 Reorder the terms: -9.583333335 + x = 8.953971808 Solving -9.583333335 + x = 8.953971808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.583333335' to each side of the equation. -9.583333335 + 9.583333335 + x = 8.953971808 + 9.583333335 Combine like terms: -9.583333335 + 9.583333335 = 0.000000000 0.000000000 + x = 8.953971808 + 9.583333335 x = 8.953971808 + 9.583333335 Combine like terms: 8.953971808 + 9.583333335 = 18.537305143 x = 18.537305143 Simplifying x = 18.537305143Subproblem 2
x + -9.583333335 = -8.953971808 Simplifying x + -9.583333335 = -8.953971808 Reorder the terms: -9.583333335 + x = -8.953971808 Solving -9.583333335 + x = -8.953971808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.583333335' to each side of the equation. -9.583333335 + 9.583333335 + x = -8.953971808 + 9.583333335 Combine like terms: -9.583333335 + 9.583333335 = 0.000000000 0.000000000 + x = -8.953971808 + 9.583333335 x = -8.953971808 + 9.583333335 Combine like terms: -8.953971808 + 9.583333335 = 0.629361527 x = 0.629361527 Simplifying x = 0.629361527Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.537305143, 0.629361527}
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