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Simplifying 5000 + -700x + 20x2 = 600 Solving 5000 + -700x + 20x2 = 600 Solving for variable 'x'. Reorder the terms: 5000 + -600 + -700x + 20x2 = 600 + -600 Combine like terms: 5000 + -600 = 4400 4400 + -700x + 20x2 = 600 + -600 Combine like terms: 600 + -600 = 0 4400 + -700x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(220 + -35x + x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(220 + -35x + x2)' equal to zero and attempt to solve: Simplifying 220 + -35x + x2 = 0 Solving 220 + -35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-220' to each side of the equation. 220 + -35x + -220 + x2 = 0 + -220 Reorder the terms: 220 + -220 + -35x + x2 = 0 + -220 Combine like terms: 220 + -220 = 0 0 + -35x + x2 = 0 + -220 -35x + x2 = 0 + -220 Combine like terms: 0 + -220 = -220 -35x + x2 = -220 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = -220 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -220 + 306.25 Combine like terms: -220 + 306.25 = 86.25 306.25 + -35x + x2 = 86.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + -17.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + -17.5 = 9.287087811 Simplifying x + -17.5 = 9.287087811 Reorder the terms: -17.5 + x = 9.287087811 Solving -17.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 9.287087811 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 9.287087811 + 17.5 x = 9.287087811 + 17.5 Combine like terms: 9.287087811 + 17.5 = 26.787087811 x = 26.787087811 Simplifying x = 26.787087811Subproblem 2
x + -17.5 = -9.287087811 Simplifying x + -17.5 = -9.287087811 Reorder the terms: -17.5 + x = -9.287087811 Solving -17.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -9.287087811 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -9.287087811 + 17.5 x = -9.287087811 + 17.5 Combine like terms: -9.287087811 + 17.5 = 8.212912189 x = 8.212912189 Simplifying x = 8.212912189Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.787087811, 8.212912189}Solution
x = {26.787087811, 8.212912189}
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