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Simplifying 16x2 + -1x + -3600 = 0 Reorder the terms: -3600 + -1x + 16x2 = 0 Solving -3600 + -1x + 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'. -225 + -0.0625x + x2 = 0 Move the constant term to the right: Add '225' to each side of the equation. -225 + -0.0625x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + -0.0625x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + -0.0625x + x2 = 0 + 225 -0.0625x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 -0.0625x + x2 = 225 The x term is -0.0625x. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625x + 0.0009765625 + x2 = 225 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625x + x2 = 225 + 0.0009765625 Combine like terms: 225 + 0.0009765625 = 225.0009765625 0.0009765625 + -0.0625x + x2 = 225.0009765625 Factor a perfect square on the left side: (x + -0.03125)(x + -0.03125) = 225.0009765625 Calculate the square root of the right side: 15.000032552 Break this problem into two subproblems by setting (x + -0.03125) equal to 15.000032552 and -15.000032552.Subproblem 1
x + -0.03125 = 15.000032552 Simplifying x + -0.03125 = 15.000032552 Reorder the terms: -0.03125 + x = 15.000032552 Solving -0.03125 + x = 15.000032552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = 15.000032552 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = 15.000032552 + 0.03125 x = 15.000032552 + 0.03125 Combine like terms: 15.000032552 + 0.03125 = 15.031282552 x = 15.031282552 Simplifying x = 15.031282552Subproblem 2
x + -0.03125 = -15.000032552 Simplifying x + -0.03125 = -15.000032552 Reorder the terms: -0.03125 + x = -15.000032552 Solving -0.03125 + x = -15.000032552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = -15.000032552 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = -15.000032552 + 0.03125 x = -15.000032552 + 0.03125 Combine like terms: -15.000032552 + 0.03125 = -14.968782552 x = -14.968782552 Simplifying x = -14.968782552Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.031282552, -14.968782552}
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