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Simplifying -16x2 + 48x + 5 = 0 Reorder the terms: 5 + 48x + -16x2 = 0 Solving 5 + 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'. -0.3125 + -3x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -3x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -3x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -3x + x2 = 0 + 0.3125 -3x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -3x + x2 = 0.3125 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 = 0.3125 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.3125 + 2.25 Combine like terms: 0.3125 + 2.25 = 2.5625 2.25 + -3x + x2 = 2.5625 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -1.5) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -1.5 = 1.600781059 Simplifying x + -1.5 = 1.600781059 Reorder the terms: -1.5 + x = 1.600781059 Solving -1.5 + x = 1.600781059 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 = 1.600781059 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.600781059 + 1.5 x = 1.600781059 + 1.5 Combine like terms: 1.600781059 + 1.5 = 3.100781059 x = 3.100781059 Simplifying x = 3.100781059Subproblem 2
x + -1.5 = -1.600781059 Simplifying x + -1.5 = -1.600781059 Reorder the terms: -1.5 + x = -1.600781059 Solving -1.5 + x = -1.600781059 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 = -1.600781059 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.600781059 + 1.5 x = -1.600781059 + 1.5 Combine like terms: -1.600781059 + 1.5 = -0.100781059 x = -0.100781059 Simplifying x = -0.100781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.100781059, -0.100781059}
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