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Simplifying 50.4 = 2.5x(15 + -1x) + -2 50.4 = (15 * 2.5x + -1x * 2.5x) + -2 50.4 = (37.5x + -2.5x2) + -2 Reorder the terms: 50.4 = -2 + 37.5x + -2.5x2 Solving 50.4 = -2 + 37.5x + -2.5x2 Solving for variable 'x'. Combine like terms: 50.4 + 2 = 52.4 52.4 + -37.5x + 2.5x2 = -2 + 37.5x + -2.5x2 + 2 + -37.5x + 2.5x2 Reorder the terms: 52.4 + -37.5x + 2.5x2 = -2 + 2 + 37.5x + -37.5x + -2.5x2 + 2.5x2 Combine like terms: -2 + 2 = 0 52.4 + -37.5x + 2.5x2 = 0 + 37.5x + -37.5x + -2.5x2 + 2.5x2 52.4 + -37.5x + 2.5x2 = 37.5x + -37.5x + -2.5x2 + 2.5x2 Combine like terms: 37.5x + -37.5x = 0.0 52.4 + -37.5x + 2.5x2 = 0.0 + -2.5x2 + 2.5x2 52.4 + -37.5x + 2.5x2 = -2.5x2 + 2.5x2 Combine like terms: -2.5x2 + 2.5x2 = 0.0 52.4 + -37.5x + 2.5x2 = 0.0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 20.96 + -15x + x2 = 0 Move the constant term to the right: Add '-20.96' to each side of the equation. 20.96 + -15x + -20.96 + x2 = 0 + -20.96 Reorder the terms: 20.96 + -20.96 + -15x + x2 = 0 + -20.96 Combine like terms: 20.96 + -20.96 = 0.00 0.00 + -15x + x2 = 0 + -20.96 -15x + x2 = 0 + -20.96 Combine like terms: 0 + -20.96 = -20.96 -15x + x2 = -20.96 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -20.96 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -20.96 + 56.25 Combine like terms: -20.96 + 56.25 = 35.29 56.25 + -15x + x2 = 35.29 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 35.29 Calculate the square root of the right side: 5.940538696 Break this problem into two subproblems by setting (x + -7.5) equal to 5.940538696 and -5.940538696.Subproblem 1
x + -7.5 = 5.940538696 Simplifying x + -7.5 = 5.940538696 Reorder the terms: -7.5 + x = 5.940538696 Solving -7.5 + x = 5.940538696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 5.940538696 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 5.940538696 + 7.5 x = 5.940538696 + 7.5 Combine like terms: 5.940538696 + 7.5 = 13.440538696 x = 13.440538696 Simplifying x = 13.440538696Subproblem 2
x + -7.5 = -5.940538696 Simplifying x + -7.5 = -5.940538696 Reorder the terms: -7.5 + x = -5.940538696 Solving -7.5 + x = -5.940538696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -5.940538696 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -5.940538696 + 7.5 x = -5.940538696 + 7.5 Combine like terms: -5.940538696 + 7.5 = 1.559461304 x = 1.559461304 Simplifying x = 1.559461304Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.440538696, 1.559461304}
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