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Simplifying -16x2 + 128x + 3 = 0 Reorder the terms: 3 + 128x + -16x2 = 0 Solving 3 + 128x + -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'. -0.1875 + -8x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -8x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -8x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -8x + x2 = 0 + 0.1875 -8x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -8x + x2 = 0.1875 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 0.1875 + 16 Reorder the terms: 16 + -8x + x2 = 0.1875 + 16 Combine like terms: 0.1875 + 16 = 16.1875 16 + -8x + x2 = 16.1875 Factor a perfect square on the left side: (x + -4)(x + -4) = 16.1875 Calculate the square root of the right side: 4.023369235 Break this problem into two subproblems by setting (x + -4) equal to 4.023369235 and -4.023369235.Subproblem 1
x + -4 = 4.023369235 Simplifying x + -4 = 4.023369235 Reorder the terms: -4 + x = 4.023369235 Solving -4 + x = 4.023369235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.023369235 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.023369235 + 4 x = 4.023369235 + 4 Combine like terms: 4.023369235 + 4 = 8.023369235 x = 8.023369235 Simplifying x = 8.023369235Subproblem 2
x + -4 = -4.023369235 Simplifying x + -4 = -4.023369235 Reorder the terms: -4 + x = -4.023369235 Solving -4 + x = -4.023369235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.023369235 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.023369235 + 4 x = -4.023369235 + 4 Combine like terms: -4.023369235 + 4 = -0.023369235 x = -0.023369235 Simplifying x = -0.023369235Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.023369235, -0.023369235}
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