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Simplifying 100x2 + -500x = 8000 Reorder the terms: -500x + 100x2 = 8000 Solving -500x + 100x2 = 8000 Solving for variable 'x'. Reorder the terms: -8000 + -500x + 100x2 = 8000 + -8000 Combine like terms: 8000 + -8000 = 0 -8000 + -500x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(-80 + -5x + x2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(-80 + -5x + x2)' equal to zero and attempt to solve: Simplifying -80 + -5x + x2 = 0 Solving -80 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -5x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -5x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -5x + x2 = 0 + 80 -5x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -5x + x2 = 80 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 80 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 80 + 6.25 Combine like terms: 80 + 6.25 = 86.25 6.25 + -5x + x2 = 86.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + -2.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + -2.5 = 9.287087811 Simplifying x + -2.5 = 9.287087811 Reorder the terms: -2.5 + x = 9.287087811 Solving -2.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 9.287087811 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 9.287087811 + 2.5 x = 9.287087811 + 2.5 Combine like terms: 9.287087811 + 2.5 = 11.787087811 x = 11.787087811 Simplifying x = 11.787087811Subproblem 2
x + -2.5 = -9.287087811 Simplifying x + -2.5 = -9.287087811 Reorder the terms: -2.5 + x = -9.287087811 Solving -2.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -9.287087811 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -9.287087811 + 2.5 x = -9.287087811 + 2.5 Combine like terms: -9.287087811 + 2.5 = -6.787087811 x = -6.787087811 Simplifying x = -6.787087811Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.787087811, -6.787087811}Solution
x = {11.787087811, -6.787087811}
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