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Simplifying -443.432625675216x2 + -39.671192x + 1 = 0 Reorder the terms: 1 + -39.671192x + -443.432625675216x2 = 0 Solving 1 + -39.671192x + -443.432625675216x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -443.432625675216 the coefficient of the squared term: Divide each side by '-443.432625675216'. -0.002255134021 + 0.08946385472x + x2 = 0 Move the constant term to the right: Add '0.002255134021' to each side of the equation. -0.002255134021 + 0.08946385472x + 0.002255134021 + x2 = 0 + 0.002255134021 Reorder the terms: -0.002255134021 + 0.002255134021 + 0.08946385472x + x2 = 0 + 0.002255134021 Combine like terms: -0.002255134021 + 0.002255134021 = 0.000000000000 0.000000000000 + 0.08946385472x + x2 = 0 + 0.002255134021 0.08946385472x + x2 = 0 + 0.002255134021 Combine like terms: 0 + 0.002255134021 = 0.002255134021 0.08946385472x + x2 = 0.002255134021 The x term is 0.08946385472x. Take half its coefficient (0.04473192736). Square it (0.002000945325) and add it to both sides. Add '0.002000945325' to each side of the equation. 0.08946385472x + 0.002000945325 + x2 = 0.002255134021 + 0.002000945325 Reorder the terms: 0.002000945325 + 0.08946385472x + x2 = 0.002255134021 + 0.002000945325 Combine like terms: 0.002255134021 + 0.002000945325 = 0.004256079346 0.002000945325 + 0.08946385472x + x2 = 0.004256079346 Factor a perfect square on the left side: (x + 0.04473192736)(x + 0.04473192736) = 0.004256079346 Calculate the square root of the right side: 0.065238634 Break this problem into two subproblems by setting (x + 0.04473192736) equal to 0.065238634 and -0.065238634.Subproblem 1
x + 0.04473192736 = 0.065238634 Simplifying x + 0.04473192736 = 0.065238634 Reorder the terms: 0.04473192736 + x = 0.065238634 Solving 0.04473192736 + x = 0.065238634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04473192736' to each side of the equation. 0.04473192736 + -0.04473192736 + x = 0.065238634 + -0.04473192736 Combine like terms: 0.04473192736 + -0.04473192736 = 0.00000000000 0.00000000000 + x = 0.065238634 + -0.04473192736 x = 0.065238634 + -0.04473192736 Combine like terms: 0.065238634 + -0.04473192736 = 0.02050670664 x = 0.02050670664 Simplifying x = 0.02050670664Subproblem 2
x + 0.04473192736 = -0.065238634 Simplifying x + 0.04473192736 = -0.065238634 Reorder the terms: 0.04473192736 + x = -0.065238634 Solving 0.04473192736 + x = -0.065238634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04473192736' to each side of the equation. 0.04473192736 + -0.04473192736 + x = -0.065238634 + -0.04473192736 Combine like terms: 0.04473192736 + -0.04473192736 = 0.00000000000 0.00000000000 + x = -0.065238634 + -0.04473192736 x = -0.065238634 + -0.04473192736 Combine like terms: -0.065238634 + -0.04473192736 = -0.10997056136 x = -0.10997056136 Simplifying x = -0.10997056136Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.02050670664, -0.10997056136}
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