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Simplifying 0 = -16x2 + 63x + 92 Reorder the terms: 0 = 92 + 63x + -16x2 Solving 0 = 92 + 63x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -92 = -92 -92 + -63x + 16x2 = 92 + 63x + -16x2 + -92 + -63x + 16x2 Reorder the terms: -92 + -63x + 16x2 = 92 + -92 + 63x + -63x + -16x2 + 16x2 Combine like terms: 92 + -92 = 0 -92 + -63x + 16x2 = 0 + 63x + -63x + -16x2 + 16x2 -92 + -63x + 16x2 = 63x + -63x + -16x2 + 16x2 Combine like terms: 63x + -63x = 0 -92 + -63x + 16x2 = 0 + -16x2 + 16x2 -92 + -63x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -92 + -63x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.75 + -3.9375x + x2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + -3.9375x + 5.75 + x2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + -3.9375x + x2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + -3.9375x + x2 = 0 + 5.75 -3.9375x + x2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 -3.9375x + x2 = 5.75 The x term is -3.9375x. Take half its coefficient (-1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. -3.9375x + 3.875976563 + x2 = 5.75 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375x + x2 = 5.75 + 3.875976563 Combine like terms: 5.75 + 3.875976563 = 9.625976563 3.875976563 + -3.9375x + x2 = 9.625976563 Factor a perfect square on the left side: (x + -1.96875)(x + -1.96875) = 9.625976563 Calculate the square root of the right side: 3.102575795 Break this problem into two subproblems by setting (x + -1.96875) equal to 3.102575795 and -3.102575795.Subproblem 1
x + -1.96875 = 3.102575795 Simplifying x + -1.96875 = 3.102575795 Reorder the terms: -1.96875 + x = 3.102575795 Solving -1.96875 + x = 3.102575795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = 3.102575795 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = 3.102575795 + 1.96875 x = 3.102575795 + 1.96875 Combine like terms: 3.102575795 + 1.96875 = 5.071325795 x = 5.071325795 Simplifying x = 5.071325795Subproblem 2
x + -1.96875 = -3.102575795 Simplifying x + -1.96875 = -3.102575795 Reorder the terms: -1.96875 + x = -3.102575795 Solving -1.96875 + x = -3.102575795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = -3.102575795 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = -3.102575795 + 1.96875 x = -3.102575795 + 1.96875 Combine like terms: -3.102575795 + 1.96875 = -1.133825795 x = -1.133825795 Simplifying x = -1.133825795Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.071325795, -1.133825795}
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