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Simplifying (x)(5x + -3) = 60(3x + 2) Reorder the terms: x(-3 + 5x) = 60(3x + 2) (-3 * x + 5x * x) = 60(3x + 2) (-3x + 5x2) = 60(3x + 2) Reorder the terms: -3x + 5x2 = 60(2 + 3x) -3x + 5x2 = (2 * 60 + 3x * 60) -3x + 5x2 = (120 + 180x) Solving -3x + 5x2 = 120 + 180x Solving for variable 'x'. Reorder the terms: -120 + -3x + -180x + 5x2 = 120 + 180x + -120 + -180x Combine like terms: -3x + -180x = -183x -120 + -183x + 5x2 = 120 + 180x + -120 + -180x Reorder the terms: -120 + -183x + 5x2 = 120 + -120 + 180x + -180x Combine like terms: 120 + -120 = 0 -120 + -183x + 5x2 = 0 + 180x + -180x -120 + -183x + 5x2 = 180x + -180x Combine like terms: 180x + -180x = 0 -120 + -183x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -24 + -36.6x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -36.6x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -36.6x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -36.6x + x2 = 0 + 24 -36.6x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -36.6x + x2 = 24 The x term is -36.6x. Take half its coefficient (-18.3). Square it (334.89) and add it to both sides. Add '334.89' to each side of the equation. -36.6x + 334.89 + x2 = 24 + 334.89 Reorder the terms: 334.89 + -36.6x + x2 = 24 + 334.89 Combine like terms: 24 + 334.89 = 358.89 334.89 + -36.6x + x2 = 358.89 Factor a perfect square on the left side: (x + -18.3)(x + -18.3) = 358.89 Calculate the square root of the right side: 18.94439231 Break this problem into two subproblems by setting (x + -18.3) equal to 18.94439231 and -18.94439231.Subproblem 1
x + -18.3 = 18.94439231 Simplifying x + -18.3 = 18.94439231 Reorder the terms: -18.3 + x = 18.94439231 Solving -18.3 + x = 18.94439231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.3' to each side of the equation. -18.3 + 18.3 + x = 18.94439231 + 18.3 Combine like terms: -18.3 + 18.3 = 0.0 0.0 + x = 18.94439231 + 18.3 x = 18.94439231 + 18.3 Combine like terms: 18.94439231 + 18.3 = 37.24439231 x = 37.24439231 Simplifying x = 37.24439231Subproblem 2
x + -18.3 = -18.94439231 Simplifying x + -18.3 = -18.94439231 Reorder the terms: -18.3 + x = -18.94439231 Solving -18.3 + x = -18.94439231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.3' to each side of the equation. -18.3 + 18.3 + x = -18.94439231 + 18.3 Combine like terms: -18.3 + 18.3 = 0.0 0.0 + x = -18.94439231 + 18.3 x = -18.94439231 + 18.3 Combine like terms: -18.94439231 + 18.3 = -0.64439231 x = -0.64439231 Simplifying x = -0.64439231Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.24439231, -0.64439231}
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