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Simplifying 43 + x(x + 51) = 180 Reorder the terms: 43 + x(51 + x) = 180 43 + (51 * x + x * x) = 180 43 + (51x + x2) = 180 Solving 43 + 51x + x2 = 180 Solving for variable 'x'. Reorder the terms: 43 + -180 + 51x + x2 = 180 + -180 Combine like terms: 43 + -180 = -137 -137 + 51x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -137 + 51x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '137' to each side of the equation. -137 + 51x + 137 + x2 = 0 + 137 Reorder the terms: -137 + 137 + 51x + x2 = 0 + 137 Combine like terms: -137 + 137 = 0 0 + 51x + x2 = 0 + 137 51x + x2 = 0 + 137 Combine like terms: 0 + 137 = 137 51x + x2 = 137 The x term is 51x. Take half its coefficient (25.5). Square it (650.25) and add it to both sides. Add '650.25' to each side of the equation. 51x + 650.25 + x2 = 137 + 650.25 Reorder the terms: 650.25 + 51x + x2 = 137 + 650.25 Combine like terms: 137 + 650.25 = 787.25 650.25 + 51x + x2 = 787.25 Factor a perfect square on the left side: (x + 25.5)(x + 25.5) = 787.25 Calculate the square root of the right side: 28.057975693 Break this problem into two subproblems by setting (x + 25.5) equal to 28.057975693 and -28.057975693.Subproblem 1
x + 25.5 = 28.057975693 Simplifying x + 25.5 = 28.057975693 Reorder the terms: 25.5 + x = 28.057975693 Solving 25.5 + x = 28.057975693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.5' to each side of the equation. 25.5 + -25.5 + x = 28.057975693 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + x = 28.057975693 + -25.5 x = 28.057975693 + -25.5 Combine like terms: 28.057975693 + -25.5 = 2.557975693 x = 2.557975693 Simplifying x = 2.557975693Subproblem 2
x + 25.5 = -28.057975693 Simplifying x + 25.5 = -28.057975693 Reorder the terms: 25.5 + x = -28.057975693 Solving 25.5 + x = -28.057975693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.5' to each side of the equation. 25.5 + -25.5 + x = -28.057975693 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + x = -28.057975693 + -25.5 x = -28.057975693 + -25.5 Combine like terms: -28.057975693 + -25.5 = -53.557975693 x = -53.557975693 Simplifying x = -53.557975693Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.557975693, -53.557975693}
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