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Simplifying 0 = 4x2 + -100x + 1 Reorder the terms: 0 = 1 + -100x + 4x2 Solving 0 = 1 + -100x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 100x + -4x2 = 1 + -100x + 4x2 + -1 + 100x + -4x2 Reorder the terms: -1 + 100x + -4x2 = 1 + -1 + -100x + 100x + 4x2 + -4x2 Combine like terms: 1 + -1 = 0 -1 + 100x + -4x2 = 0 + -100x + 100x + 4x2 + -4x2 -1 + 100x + -4x2 = -100x + 100x + 4x2 + -4x2 Combine like terms: -100x + 100x = 0 -1 + 100x + -4x2 = 0 + 4x2 + -4x2 -1 + 100x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -1 + 100x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.25 + -25x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -25x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -25x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -25x + x2 = 0 + -0.25 -25x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -25x + x2 = -0.25 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 = -0.25 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -0.25 + 156.25 Combine like terms: -0.25 + 156.25 = 156 156.25 + -25x + x2 = 156 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + -12.5) equal to 12.489995997 and -12.489995997.Subproblem 1
x + -12.5 = 12.489995997 Simplifying x + -12.5 = 12.489995997 Reorder the terms: -12.5 + x = 12.489995997 Solving -12.5 + x = 12.489995997 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 = 12.489995997 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.489995997 + 12.5 x = 12.489995997 + 12.5 Combine like terms: 12.489995997 + 12.5 = 24.989995997 x = 24.989995997 Simplifying x = 24.989995997Subproblem 2
x + -12.5 = -12.489995997 Simplifying x + -12.5 = -12.489995997 Reorder the terms: -12.5 + x = -12.489995997 Solving -12.5 + x = -12.489995997 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 = -12.489995997 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.489995997 + 12.5 x = -12.489995997 + 12.5 Combine like terms: -12.489995997 + 12.5 = 0.010004003 x = 0.010004003 Simplifying x = 0.010004003Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.989995997, 0.010004003}
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