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Simplifying -16x2 + 33x + 46 = 0 Reorder the terms: 46 + 33x + -16x2 = 0 Solving 46 + 33x + -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'. -2.875 + -2.0625x + x2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + -2.0625x + 2.875 + x2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + -2.0625x + x2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + -2.0625x + x2 = 0 + 2.875 -2.0625x + x2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 -2.0625x + x2 = 2.875 The x term is -2.0625x. Take half its coefficient (-1.03125). Square it (1.063476563) and add it to both sides. Add '1.063476563' to each side of the equation. -2.0625x + 1.063476563 + x2 = 2.875 + 1.063476563 Reorder the terms: 1.063476563 + -2.0625x + x2 = 2.875 + 1.063476563 Combine like terms: 2.875 + 1.063476563 = 3.938476563 1.063476563 + -2.0625x + x2 = 3.938476563 Factor a perfect square on the left side: (x + -1.03125)(x + -1.03125) = 3.938476563 Calculate the square root of the right side: 1.984559539 Break this problem into two subproblems by setting (x + -1.03125) equal to 1.984559539 and -1.984559539.Subproblem 1
x + -1.03125 = 1.984559539 Simplifying x + -1.03125 = 1.984559539 Reorder the terms: -1.03125 + x = 1.984559539 Solving -1.03125 + x = 1.984559539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.03125' to each side of the equation. -1.03125 + 1.03125 + x = 1.984559539 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + x = 1.984559539 + 1.03125 x = 1.984559539 + 1.03125 Combine like terms: 1.984559539 + 1.03125 = 3.015809539 x = 3.015809539 Simplifying x = 3.015809539Subproblem 2
x + -1.03125 = -1.984559539 Simplifying x + -1.03125 = -1.984559539 Reorder the terms: -1.03125 + x = -1.984559539 Solving -1.03125 + x = -1.984559539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.03125' to each side of the equation. -1.03125 + 1.03125 + x = -1.984559539 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + x = -1.984559539 + 1.03125 x = -1.984559539 + 1.03125 Combine like terms: -1.984559539 + 1.03125 = -0.953309539 x = -0.953309539 Simplifying x = -0.953309539Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.015809539, -0.953309539}
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