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Simplifying 16X2 + -55X + 10 = 0 Reorder the terms: 10 + -55X + 16X2 = 0 Solving 10 + -55X + 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'. 0.625 + -3.4375X + X2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -3.4375X + -0.625 + X2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -3.4375X + X2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -3.4375X + X2 = 0 + -0.625 -3.4375X + X2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -3.4375X + X2 = -0.625 The X term is -3.4375X. Take half its coefficient (-1.71875). Square it (2.954101563) and add it to both sides. Add '2.954101563' to each side of the equation. -3.4375X + 2.954101563 + X2 = -0.625 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375X + X2 = -0.625 + 2.954101563 Combine like terms: -0.625 + 2.954101563 = 2.329101563 2.954101563 + -3.4375X + X2 = 2.329101563 Factor a perfect square on the left side: (X + -1.71875)(X + -1.71875) = 2.329101563 Calculate the square root of the right side: 1.526139431 Break this problem into two subproblems by setting (X + -1.71875) equal to 1.526139431 and -1.526139431.Subproblem 1
X + -1.71875 = 1.526139431 Simplifying X + -1.71875 = 1.526139431 Reorder the terms: -1.71875 + X = 1.526139431 Solving -1.71875 + X = 1.526139431 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + X = 1.526139431 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + X = 1.526139431 + 1.71875 X = 1.526139431 + 1.71875 Combine like terms: 1.526139431 + 1.71875 = 3.244889431 X = 3.244889431 Simplifying X = 3.244889431Subproblem 2
X + -1.71875 = -1.526139431 Simplifying X + -1.71875 = -1.526139431 Reorder the terms: -1.71875 + X = -1.526139431 Solving -1.71875 + X = -1.526139431 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + X = -1.526139431 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + X = -1.526139431 + 1.71875 X = -1.526139431 + 1.71875 Combine like terms: -1.526139431 + 1.71875 = 0.192610569 X = 0.192610569 Simplifying X = 0.192610569Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.244889431, 0.192610569}
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