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Simplifying (x + -28) + (2x + -16)(0.5x + 14) = 180 Reorder the terms: (-28 + x) + (2x + -16)(0.5x + 14) = 180 Remove parenthesis around (-28 + x) -28 + x + (2x + -16)(0.5x + 14) = 180 Reorder the terms: -28 + x + (-16 + 2x)(0.5x + 14) = 180 Reorder the terms: -28 + x + (-16 + 2x)(14 + 0.5x) = 180 Multiply (-16 + 2x) * (14 + 0.5x) -28 + x + (-16(14 + 0.5x) + 2x * (14 + 0.5x)) = 180 -28 + x + ((14 * -16 + 0.5x * -16) + 2x * (14 + 0.5x)) = 180 -28 + x + ((-224 + -8x) + 2x * (14 + 0.5x)) = 180 -28 + x + (-224 + -8x + (14 * 2x + 0.5x * 2x)) = 180 -28 + x + (-224 + -8x + (28x + 1x2)) = 180 Combine like terms: -8x + 28x = 20x -28 + x + (-224 + 20x + 1x2) = 180 Reorder the terms: -28 + -224 + x + 20x + 1x2 = 180 Combine like terms: -28 + -224 = -252 -252 + x + 20x + 1x2 = 180 Combine like terms: x + 20x = 21x -252 + 21x + 1x2 = 180 Solving -252 + 21x + 1x2 = 180 Solving for variable 'x'. Reorder the terms: -252 + -180 + 21x + 1x2 = 180 + -180 Combine like terms: -252 + -180 = -432 -432 + 21x + 1x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -432 + 21x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '432' to each side of the equation. -432 + 21x + 432 + x2 = 0 + 432 Reorder the terms: -432 + 432 + 21x + x2 = 0 + 432 Combine like terms: -432 + 432 = 0 0 + 21x + x2 = 0 + 432 21x + x2 = 0 + 432 Combine like terms: 0 + 432 = 432 21x + x2 = 432 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = 432 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 432 + 110.25 Combine like terms: 432 + 110.25 = 542.25 110.25 + 21x + x2 = 542.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 542.25 Calculate the square root of the right side: 23.286262044 Break this problem into two subproblems by setting (x + 10.5) equal to 23.286262044 and -23.286262044.Subproblem 1
x + 10.5 = 23.286262044 Simplifying x + 10.5 = 23.286262044 Reorder the terms: 10.5 + x = 23.286262044 Solving 10.5 + x = 23.286262044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 23.286262044 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 23.286262044 + -10.5 x = 23.286262044 + -10.5 Combine like terms: 23.286262044 + -10.5 = 12.786262044 x = 12.786262044 Simplifying x = 12.786262044Subproblem 2
x + 10.5 = -23.286262044 Simplifying x + 10.5 = -23.286262044 Reorder the terms: 10.5 + x = -23.286262044 Solving 10.5 + x = -23.286262044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -23.286262044 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -23.286262044 + -10.5 x = -23.286262044 + -10.5 Combine like terms: -23.286262044 + -10.5 = -33.786262044 x = -33.786262044 Simplifying x = -33.786262044Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.786262044, -33.786262044}
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