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Simplifying x = -16x2 + 200x + 4 Reorder the terms: x = 4 + 200x + -16x2 Solving x = 4 + 200x + -16x2 Solving for variable 'x'. Reorder the terms: -4 + x + -200x + 16x2 = 4 + 200x + -16x2 + -4 + -200x + 16x2 Combine like terms: x + -200x = -199x -4 + -199x + 16x2 = 4 + 200x + -16x2 + -4 + -200x + 16x2 Reorder the terms: -4 + -199x + 16x2 = 4 + -4 + 200x + -200x + -16x2 + 16x2 Combine like terms: 4 + -4 = 0 -4 + -199x + 16x2 = 0 + 200x + -200x + -16x2 + 16x2 -4 + -199x + 16x2 = 200x + -200x + -16x2 + 16x2 Combine like terms: 200x + -200x = 0 -4 + -199x + 16x2 = 0 + -16x2 + 16x2 -4 + -199x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -4 + -199x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + -12.4375x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -12.4375x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -12.4375x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -12.4375x + x2 = 0 + 0.25 -12.4375x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -12.4375x + x2 = 0.25 The x term is -12.4375x. Take half its coefficient (-6.21875). Square it (38.67285156) and add it to both sides. Add '38.67285156' to each side of the equation. -12.4375x + 38.67285156 + x2 = 0.25 + 38.67285156 Reorder the terms: 38.67285156 + -12.4375x + x2 = 0.25 + 38.67285156 Combine like terms: 0.25 + 38.67285156 = 38.92285156 38.67285156 + -12.4375x + x2 = 38.92285156 Factor a perfect square on the left side: (x + -6.21875)(x + -6.21875) = 38.92285156 Calculate the square root of the right side: 6.238818122 Break this problem into two subproblems by setting (x + -6.21875) equal to 6.238818122 and -6.238818122.Subproblem 1
x + -6.21875 = 6.238818122 Simplifying x + -6.21875 = 6.238818122 Reorder the terms: -6.21875 + x = 6.238818122 Solving -6.21875 + x = 6.238818122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.21875' to each side of the equation. -6.21875 + 6.21875 + x = 6.238818122 + 6.21875 Combine like terms: -6.21875 + 6.21875 = 0.00000 0.00000 + x = 6.238818122 + 6.21875 x = 6.238818122 + 6.21875 Combine like terms: 6.238818122 + 6.21875 = 12.457568122 x = 12.457568122 Simplifying x = 12.457568122Subproblem 2
x + -6.21875 = -6.238818122 Simplifying x + -6.21875 = -6.238818122 Reorder the terms: -6.21875 + x = -6.238818122 Solving -6.21875 + x = -6.238818122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.21875' to each side of the equation. -6.21875 + 6.21875 + x = -6.238818122 + 6.21875 Combine like terms: -6.21875 + 6.21875 = 0.00000 0.00000 + x = -6.238818122 + 6.21875 x = -6.238818122 + 6.21875 Combine like terms: -6.238818122 + 6.21875 = -0.020068122 x = -0.020068122 Simplifying x = -0.020068122Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.457568122, -0.020068122}
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