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Simplifying (x + 2.8)(37.2 + -2x) = 50 Reorder the terms: (2.8 + x)(37.2 + -2x) = 50 Multiply (2.8 + x) * (37.2 + -2x) (2.8(37.2 + -2x) + x(37.2 + -2x)) = 50 ((37.2 * 2.8 + -2x * 2.8) + x(37.2 + -2x)) = 50 ((104.16 + -5.6x) + x(37.2 + -2x)) = 50 (104.16 + -5.6x + (37.2 * x + -2x * x)) = 50 (104.16 + -5.6x + (37.2x + -2x2)) = 50 Combine like terms: -5.6x + 37.2x = 31.6x (104.16 + 31.6x + -2x2) = 50 Solving 104.16 + 31.6x + -2x2 = 50 Solving for variable 'x'. Reorder the terms: 104.16 + -50 + 31.6x + -2x2 = 50 + -50 Combine like terms: 104.16 + -50 = 54.16 54.16 + 31.6x + -2x2 = 50 + -50 Combine like terms: 50 + -50 = 0 54.16 + 31.6x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -27.08 + -15.8x + x2 = 0 Move the constant term to the right: Add '27.08' to each side of the equation. -27.08 + -15.8x + 27.08 + x2 = 0 + 27.08 Reorder the terms: -27.08 + 27.08 + -15.8x + x2 = 0 + 27.08 Combine like terms: -27.08 + 27.08 = 0.00 0.00 + -15.8x + x2 = 0 + 27.08 -15.8x + x2 = 0 + 27.08 Combine like terms: 0 + 27.08 = 27.08 -15.8x + x2 = 27.08 The x term is -15.8x. Take half its coefficient (-7.9). Square it (62.41) and add it to both sides. Add '62.41' to each side of the equation. -15.8x + 62.41 + x2 = 27.08 + 62.41 Reorder the terms: 62.41 + -15.8x + x2 = 27.08 + 62.41 Combine like terms: 27.08 + 62.41 = 89.49 62.41 + -15.8x + x2 = 89.49 Factor a perfect square on the left side: (x + -7.9)(x + -7.9) = 89.49 Calculate the square root of the right side: 9.459915433 Break this problem into two subproblems by setting (x + -7.9) equal to 9.459915433 and -9.459915433.Subproblem 1
x + -7.9 = 9.459915433 Simplifying x + -7.9 = 9.459915433 Reorder the terms: -7.9 + x = 9.459915433 Solving -7.9 + x = 9.459915433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.9' to each side of the equation. -7.9 + 7.9 + x = 9.459915433 + 7.9 Combine like terms: -7.9 + 7.9 = 0.0 0.0 + x = 9.459915433 + 7.9 x = 9.459915433 + 7.9 Combine like terms: 9.459915433 + 7.9 = 17.359915433 x = 17.359915433 Simplifying x = 17.359915433Subproblem 2
x + -7.9 = -9.459915433 Simplifying x + -7.9 = -9.459915433 Reorder the terms: -7.9 + x = -9.459915433 Solving -7.9 + x = -9.459915433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.9' to each side of the equation. -7.9 + 7.9 + x = -9.459915433 + 7.9 Combine like terms: -7.9 + 7.9 = 0.0 0.0 + x = -9.459915433 + 7.9 x = -9.459915433 + 7.9 Combine like terms: -9.459915433 + 7.9 = -1.559915433 x = -1.559915433 Simplifying x = -1.559915433Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.359915433, -1.559915433}
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