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Simplifying -16x2 + 200x + 57 = 0 Reorder the terms: 57 + 200x + -16x2 = 0 Solving 57 + 200x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -3.5625 + -12.5x + x2 = 0 Move the constant term to the right: Add '3.5625' to each side of the equation. -3.5625 + -12.5x + 3.5625 + x2 = 0 + 3.5625 Reorder the terms: -3.5625 + 3.5625 + -12.5x + x2 = 0 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + -12.5x + x2 = 0 + 3.5625 -12.5x + x2 = 0 + 3.5625 Combine like terms: 0 + 3.5625 = 3.5625 -12.5x + x2 = 3.5625 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 = 3.5625 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 3.5625 + 39.0625 Combine like terms: 3.5625 + 39.0625 = 42.625 39.0625 + -12.5x + x2 = 42.625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 42.625 Calculate the square root of the right side: 6.528782429 Break this problem into two subproblems by setting (x + -6.25) equal to 6.528782429 and -6.528782429.Subproblem 1
x + -6.25 = 6.528782429 Simplifying x + -6.25 = 6.528782429 Reorder the terms: -6.25 + x = 6.528782429 Solving -6.25 + x = 6.528782429 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 = 6.528782429 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 6.528782429 + 6.25 x = 6.528782429 + 6.25 Combine like terms: 6.528782429 + 6.25 = 12.778782429 x = 12.778782429 Simplifying x = 12.778782429Subproblem 2
x + -6.25 = -6.528782429 Simplifying x + -6.25 = -6.528782429 Reorder the terms: -6.25 + x = -6.528782429 Solving -6.25 + x = -6.528782429 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 = -6.528782429 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -6.528782429 + 6.25 x = -6.528782429 + 6.25 Combine like terms: -6.528782429 + 6.25 = -0.278782429 x = -0.278782429 Simplifying x = -0.278782429Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.778782429, -0.278782429}
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