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Simplifying 16x(x + -2) + -1(x + -16) = 29 Reorder the terms: 16x(-2 + x) + -1(x + -16) = 29 (-2 * 16x + x * 16x) + -1(x + -16) = 29 (-32x + 16x2) + -1(x + -16) = 29 Reorder the terms: -32x + 16x2 + -1(-16 + x) = 29 -32x + 16x2 + (-16 * -1 + x * -1) = 29 -32x + 16x2 + (16 + -1x) = 29 Reorder the terms: 16 + -32x + -1x + 16x2 = 29 Combine like terms: -32x + -1x = -33x 16 + -33x + 16x2 = 29 Solving 16 + -33x + 16x2 = 29 Solving for variable 'x'. Reorder the terms: 16 + -29 + -33x + 16x2 = 29 + -29 Combine like terms: 16 + -29 = -13 -13 + -33x + 16x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -13 + -33x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.8125 + -2.0625x + x2 = 0 Move the constant term to the right: Add '0.8125' to each side of the equation. -0.8125 + -2.0625x + 0.8125 + x2 = 0 + 0.8125 Reorder the terms: -0.8125 + 0.8125 + -2.0625x + x2 = 0 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + -2.0625x + x2 = 0 + 0.8125 -2.0625x + x2 = 0 + 0.8125 Combine like terms: 0 + 0.8125 = 0.8125 -2.0625x + x2 = 0.8125 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 = 0.8125 + 1.063476563 Reorder the terms: 1.063476563 + -2.0625x + x2 = 0.8125 + 1.063476563 Combine like terms: 0.8125 + 1.063476563 = 1.875976563 1.063476563 + -2.0625x + x2 = 1.875976563 Factor a perfect square on the left side: (x + -1.03125)(x + -1.03125) = 1.875976563 Calculate the square root of the right side: 1.369662938 Break this problem into two subproblems by setting (x + -1.03125) equal to 1.369662938 and -1.369662938.Subproblem 1
x + -1.03125 = 1.369662938 Simplifying x + -1.03125 = 1.369662938 Reorder the terms: -1.03125 + x = 1.369662938 Solving -1.03125 + x = 1.369662938 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 = 1.369662938 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + x = 1.369662938 + 1.03125 x = 1.369662938 + 1.03125 Combine like terms: 1.369662938 + 1.03125 = 2.400912938 x = 2.400912938 Simplifying x = 2.400912938Subproblem 2
x + -1.03125 = -1.369662938 Simplifying x + -1.03125 = -1.369662938 Reorder the terms: -1.03125 + x = -1.369662938 Solving -1.03125 + x = -1.369662938 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 = -1.369662938 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + x = -1.369662938 + 1.03125 x = -1.369662938 + 1.03125 Combine like terms: -1.369662938 + 1.03125 = -0.338412938 x = -0.338412938 Simplifying x = -0.338412938Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.400912938, -0.338412938}
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