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Simplifying 16x2 + -28x + -5 = 0 Reorder the terms: -5 + -28x + 16x2 = 0 Solving -5 + -28x + 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 + -1.75x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -1.75x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -1.75x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -1.75x + x2 = 0 + 0.3125 -1.75x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -1.75x + x2 = 0.3125 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 0.3125 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 0.3125 + 0.765625 Combine like terms: 0.3125 + 0.765625 = 1.078125 0.765625 + -1.75x + x2 = 1.078125 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 1.078125 Calculate the square root of the right side: 1.038327983 Break this problem into two subproblems by setting (x + -0.875) equal to 1.038327983 and -1.038327983.Subproblem 1
x + -0.875 = 1.038327983 Simplifying x + -0.875 = 1.038327983 Reorder the terms: -0.875 + x = 1.038327983 Solving -0.875 + x = 1.038327983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 1.038327983 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.038327983 + 0.875 x = 1.038327983 + 0.875 Combine like terms: 1.038327983 + 0.875 = 1.913327983 x = 1.913327983 Simplifying x = 1.913327983Subproblem 2
x + -0.875 = -1.038327983 Simplifying x + -0.875 = -1.038327983 Reorder the terms: -0.875 + x = -1.038327983 Solving -0.875 + x = -1.038327983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -1.038327983 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.038327983 + 0.875 x = -1.038327983 + 0.875 Combine like terms: -1.038327983 + 0.875 = -0.163327983 x = -0.163327983 Simplifying x = -0.163327983Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.913327983, -0.163327983}
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