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Simplifying 20 = 100x + -4x2 Solving 20 = 100x + -4x2 Solving for variable 'x'. Reorder the terms: 20 + -100x + 4x2 = 100x + -100x + -4x2 + 4x2 Combine like terms: 100x + -100x = 0 20 + -100x + 4x2 = 0 + -4x2 + 4x2 20 + -100x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 20 + -100x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -25x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -25x + x2)' equal to zero and attempt to solve: Simplifying 5 + -25x + x2 = 0 Solving 5 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -25x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -25x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -25x + x2 = 0 + -5 -25x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -25x + x2 = -5 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -5 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -5 + 156.25 Combine like terms: -5 + 156.25 = 151.25 156.25 + -25x + x2 = 151.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 151.25 Calculate the square root of the right side: 12.298373876 Break this problem into two subproblems by setting (x + -12.5) equal to 12.298373876 and -12.298373876.Subproblem 1
x + -12.5 = 12.298373876 Simplifying x + -12.5 = 12.298373876 Reorder the terms: -12.5 + x = 12.298373876 Solving -12.5 + x = 12.298373876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 12.298373876 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.298373876 + 12.5 x = 12.298373876 + 12.5 Combine like terms: 12.298373876 + 12.5 = 24.798373876 x = 24.798373876 Simplifying x = 24.798373876Subproblem 2
x + -12.5 = -12.298373876 Simplifying x + -12.5 = -12.298373876 Reorder the terms: -12.5 + x = -12.298373876 Solving -12.5 + x = -12.298373876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -12.298373876 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.298373876 + 12.5 x = -12.298373876 + 12.5 Combine like terms: -12.298373876 + 12.5 = 0.201626124 x = 0.201626124 Simplifying x = 0.201626124Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.798373876, 0.201626124}Solution
x = {24.798373876, 0.201626124}
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