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Simplifying 0 = 16x2 + -63.5x + 41 Reorder the terms: 0 = 41 + -63.5x + 16x2 Solving 0 = 41 + -63.5x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -41 = -41 -41 + 63.5x + -16x2 = 41 + -63.5x + 16x2 + -41 + 63.5x + -16x2 Reorder the terms: -41 + 63.5x + -16x2 = 41 + -41 + -63.5x + 63.5x + 16x2 + -16x2 Combine like terms: 41 + -41 = 0 -41 + 63.5x + -16x2 = 0 + -63.5x + 63.5x + 16x2 + -16x2 -41 + 63.5x + -16x2 = -63.5x + 63.5x + 16x2 + -16x2 Combine like terms: -63.5x + 63.5x = 0.0 -41 + 63.5x + -16x2 = 0.0 + 16x2 + -16x2 -41 + 63.5x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -41 + 63.5x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 2.5625 + -3.96875x + x2 = 0 Move the constant term to the right: Add '-2.5625' to each side of the equation. 2.5625 + -3.96875x + -2.5625 + x2 = 0 + -2.5625 Reorder the terms: 2.5625 + -2.5625 + -3.96875x + x2 = 0 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + -3.96875x + x2 = 0 + -2.5625 -3.96875x + x2 = 0 + -2.5625 Combine like terms: 0 + -2.5625 = -2.5625 -3.96875x + x2 = -2.5625 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 = -2.5625 + 3.937744141 Reorder the terms: 3.937744141 + -3.96875x + x2 = -2.5625 + 3.937744141 Combine like terms: -2.5625 + 3.937744141 = 1.375244141 3.937744141 + -3.96875x + x2 = 1.375244141 Factor a perfect square on the left side: (x + -1.984375)(x + -1.984375) = 1.375244141 Calculate the square root of the right side: 1.172708037 Break this problem into two subproblems by setting (x + -1.984375) equal to 1.172708037 and -1.172708037.Subproblem 1
x + -1.984375 = 1.172708037 Simplifying x + -1.984375 = 1.172708037 Reorder the terms: -1.984375 + x = 1.172708037 Solving -1.984375 + x = 1.172708037 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 = 1.172708037 + 1.984375 Combine like terms: -1.984375 + 1.984375 = 0.000000 0.000000 + x = 1.172708037 + 1.984375 x = 1.172708037 + 1.984375 Combine like terms: 1.172708037 + 1.984375 = 3.157083037 x = 3.157083037 Simplifying x = 3.157083037Subproblem 2
x + -1.984375 = -1.172708037 Simplifying x + -1.984375 = -1.172708037 Reorder the terms: -1.984375 + x = -1.172708037 Solving -1.984375 + x = -1.172708037 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 = -1.172708037 + 1.984375 Combine like terms: -1.984375 + 1.984375 = 0.000000 0.000000 + x = -1.172708037 + 1.984375 x = -1.172708037 + 1.984375 Combine like terms: -1.172708037 + 1.984375 = 0.811666963 x = 0.811666963 Simplifying x = 0.811666963Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.157083037, 0.811666963}
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