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Simplifying 0 = -16x2 + 200x + 5 Reorder the terms: 0 = 5 + 200x + -16x2 Solving 0 = 5 + 200x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -200x + 16x2 = 5 + 200x + -16x2 + -5 + -200x + 16x2 Reorder the terms: -5 + -200x + 16x2 = 5 + -5 + 200x + -200x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 -5 + -200x + 16x2 = 0 + 200x + -200x + -16x2 + 16x2 -5 + -200x + 16x2 = 200x + -200x + -16x2 + 16x2 Combine like terms: 200x + -200x = 0 -5 + -200x + 16x2 = 0 + -16x2 + 16x2 -5 + -200x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -5 + -200x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -12.5x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -12.5x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -12.5x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -12.5x + x2 = 0 + 0.3125 -12.5x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -12.5x + x2 = 0.3125 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 0.3125 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 0.3125 + 39.0625 Combine like terms: 0.3125 + 39.0625 = 39.375 39.0625 + -12.5x + x2 = 39.375 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 39.375 Calculate the square root of the right side: 6.274950199 Break this problem into two subproblems by setting (x + -6.25) equal to 6.274950199 and -6.274950199.Subproblem 1
x + -6.25 = 6.274950199 Simplifying x + -6.25 = 6.274950199 Reorder the terms: -6.25 + x = 6.274950199 Solving -6.25 + x = 6.274950199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 6.274950199 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 6.274950199 + 6.25 x = 6.274950199 + 6.25 Combine like terms: 6.274950199 + 6.25 = 12.524950199 x = 12.524950199 Simplifying x = 12.524950199Subproblem 2
x + -6.25 = -6.274950199 Simplifying x + -6.25 = -6.274950199 Reorder the terms: -6.25 + x = -6.274950199 Solving -6.25 + x = -6.274950199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -6.274950199 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -6.274950199 + 6.25 x = -6.274950199 + 6.25 Combine like terms: -6.274950199 + 6.25 = -0.024950199 x = -0.024950199 Simplifying x = -0.024950199Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.524950199, -0.024950199}
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