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Simplifying -16x2 + -1x + 225 = 0 Reorder the terms: 225 + -1x + -16x2 = 0 Solving 225 + -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'. -14.0625 + 0.0625x + x2 = 0 Move the constant term to the right: Add '14.0625' to each side of the equation. -14.0625 + 0.0625x + 14.0625 + x2 = 0 + 14.0625 Reorder the terms: -14.0625 + 14.0625 + 0.0625x + x2 = 0 + 14.0625 Combine like terms: -14.0625 + 14.0625 = 0.0000 0.0000 + 0.0625x + x2 = 0 + 14.0625 0.0625x + x2 = 0 + 14.0625 Combine like terms: 0 + 14.0625 = 14.0625 0.0625x + x2 = 14.0625 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 = 14.0625 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625x + x2 = 14.0625 + 0.0009765625 Combine like terms: 14.0625 + 0.0009765625 = 14.0634765625 0.0009765625 + 0.0625x + x2 = 14.0634765625 Factor a perfect square on the left side: (x + 0.03125)(x + 0.03125) = 14.0634765625 Calculate the square root of the right side: 3.750130206 Break this problem into two subproblems by setting (x + 0.03125) equal to 3.750130206 and -3.750130206.Subproblem 1
x + 0.03125 = 3.750130206 Simplifying x + 0.03125 = 3.750130206 Reorder the terms: 0.03125 + x = 3.750130206 Solving 0.03125 + x = 3.750130206 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 = 3.750130206 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = 3.750130206 + -0.03125 x = 3.750130206 + -0.03125 Combine like terms: 3.750130206 + -0.03125 = 3.718880206 x = 3.718880206 Simplifying x = 3.718880206Subproblem 2
x + 0.03125 = -3.750130206 Simplifying x + 0.03125 = -3.750130206 Reorder the terms: 0.03125 + x = -3.750130206 Solving 0.03125 + x = -3.750130206 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 = -3.750130206 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = -3.750130206 + -0.03125 x = -3.750130206 + -0.03125 Combine like terms: -3.750130206 + -0.03125 = -3.781380206 x = -3.781380206 Simplifying x = -3.781380206Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.718880206, -3.781380206}
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