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Simplifying -16x2 + 63.5x + 2 = 0 Reorder the terms: 2 + 63.5x + -16x2 = 0 Solving 2 + 63.5x + -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'. -0.125 + -3.96875x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -3.96875x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -3.96875x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -3.96875x + x2 = 0 + 0.125 -3.96875x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -3.96875x + x2 = 0.125 The x term is -3.96875x. Take half its coefficient (-1.984375). Square it (3.937744141) and add it to both sides. Add '3.937744141' to each side of the equation. -3.96875x + 3.937744141 + x2 = 0.125 + 3.937744141 Reorder the terms: 3.937744141 + -3.96875x + x2 = 0.125 + 3.937744141 Combine like terms: 0.125 + 3.937744141 = 4.062744141 3.937744141 + -3.96875x + x2 = 4.062744141 Factor a perfect square on the left side: (x + -1.984375)(x + -1.984375) = 4.062744141 Calculate the square root of the right side: 2.015625 Break this problem into two subproblems by setting (x + -1.984375) equal to 2.015625 and -2.015625.Subproblem 1
x + -1.984375 = 2.015625 Simplifying x + -1.984375 = 2.015625 Reorder the terms: -1.984375 + x = 2.015625 Solving -1.984375 + x = 2.015625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.984375' to each side of the equation. -1.984375 + 1.984375 + x = 2.015625 + 1.984375 Combine like terms: -1.984375 + 1.984375 = 0.000000 0.000000 + x = 2.015625 + 1.984375 x = 2.015625 + 1.984375 Combine like terms: 2.015625 + 1.984375 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -1.984375 = -2.015625 Simplifying x + -1.984375 = -2.015625 Reorder the terms: -1.984375 + x = -2.015625 Solving -1.984375 + x = -2.015625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.984375' to each side of the equation. -1.984375 + 1.984375 + x = -2.015625 + 1.984375 Combine like terms: -1.984375 + 1.984375 = 0.000000 0.000000 + x = -2.015625 + 1.984375 x = -2.015625 + 1.984375 Combine like terms: -2.015625 + 1.984375 = -0.03125 x = -0.03125 Simplifying x = -0.03125Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -0.03125}
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