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Simplifying -16x2 + 48x + -25 = 0 Reorder the terms: -25 + 48x + -16x2 = 0 Solving -25 + 48x + -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'. 1.5625 + -3x + x2 = 0 Move the constant term to the right: Add '-1.5625' to each side of the equation. 1.5625 + -3x + -1.5625 + x2 = 0 + -1.5625 Reorder the terms: 1.5625 + -1.5625 + -3x + x2 = 0 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + -3x + x2 = 0 + -1.5625 -3x + x2 = 0 + -1.5625 Combine like terms: 0 + -1.5625 = -1.5625 -3x + x2 = -1.5625 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.5625 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.5625 + 2.25 Combine like terms: -1.5625 + 2.25 = 0.6875 2.25 + -3x + x2 = 0.6875 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.6875 Calculate the square root of the right side: 0.829156198 Break this problem into two subproblems by setting (x + -1.5) equal to 0.829156198 and -0.829156198.Subproblem 1
x + -1.5 = 0.829156198 Simplifying x + -1.5 = 0.829156198 Reorder the terms: -1.5 + x = 0.829156198 Solving -1.5 + x = 0.829156198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.829156198 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.829156198 + 1.5 x = 0.829156198 + 1.5 Combine like terms: 0.829156198 + 1.5 = 2.329156198 x = 2.329156198 Simplifying x = 2.329156198Subproblem 2
x + -1.5 = -0.829156198 Simplifying x + -1.5 = -0.829156198 Reorder the terms: -1.5 + x = -0.829156198 Solving -1.5 + x = -0.829156198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.829156198 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.829156198 + 1.5 x = -0.829156198 + 1.5 Combine like terms: -0.829156198 + 1.5 = 0.670843802 x = 0.670843802 Simplifying x = 0.670843802Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.329156198, 0.670843802}
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