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Simplifying -24673.20799626468x2 + 1x + 314.019418 = 0 Reorder the terms: 314.019418 + 1x + -24673.20799626468x2 = 0 Solving 314.019418 + 1x + -24673.20799626468x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -24673.20799626468 the coefficient of the squared term: Divide each side by '-24673.20799626468'. -0.01272714185 + -0.00004052979248x + x2 = 0 Move the constant term to the right: Add '0.01272714185' to each side of the equation. -0.01272714185 + -0.00004052979248x + 0.01272714185 + x2 = 0 + 0.01272714185 Reorder the terms: -0.01272714185 + 0.01272714185 + -0.00004052979248x + x2 = 0 + 0.01272714185 Combine like terms: -0.01272714185 + 0.01272714185 = 0.00000000000 0.00000000000 + -0.00004052979248x + x2 = 0 + 0.01272714185 -0.00004052979248x + x2 = 0 + 0.01272714185 Combine like terms: 0 + 0.01272714185 = 0.01272714185 -0.00004052979248x + x2 = 0.01272714185 The x term is -0.00004052979248x. Take half its coefficient (-0.00002026489624). Square it (0.0000000004106660196) and add it to both sides. Add '0.0000000004106660196' to each side of the equation. -0.00004052979248x + 0.0000000004106660196 + x2 = 0.01272714185 + 0.0000000004106660196 Reorder the terms: 0.0000000004106660196 + -0.00004052979248x + x2 = 0.01272714185 + 0.0000000004106660196 Combine like terms: 0.01272714185 + 0.0000000004106660196 = 0.0127271422606660196 0.0000000004106660196 + -0.00004052979248x + x2 = 0.0127271422606660196 Factor a perfect square on the left side: (x + -0.00002026489624)(x + -0.00002026489624) = 0.0127271422606660196 Calculate the square root of the right side: 0.112814637 Break this problem into two subproblems by setting (x + -0.00002026489624) equal to 0.112814637 and -0.112814637.Subproblem 1
x + -0.00002026489624 = 0.112814637 Simplifying x + -0.00002026489624 = 0.112814637 Reorder the terms: -0.00002026489624 + x = 0.112814637 Solving -0.00002026489624 + x = 0.112814637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00002026489624' to each side of the equation. -0.00002026489624 + 0.00002026489624 + x = 0.112814637 + 0.00002026489624 Combine like terms: -0.00002026489624 + 0.00002026489624 = 0.00000000000000 0.00000000000000 + x = 0.112814637 + 0.00002026489624 x = 0.112814637 + 0.00002026489624 Combine like terms: 0.112814637 + 0.00002026489624 = 0.11283490189624 x = 0.11283490189624 Simplifying x = 0.11283490189624Subproblem 2
x + -0.00002026489624 = -0.112814637 Simplifying x + -0.00002026489624 = -0.112814637 Reorder the terms: -0.00002026489624 + x = -0.112814637 Solving -0.00002026489624 + x = -0.112814637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00002026489624' to each side of the equation. -0.00002026489624 + 0.00002026489624 + x = -0.112814637 + 0.00002026489624 Combine like terms: -0.00002026489624 + 0.00002026489624 = 0.00000000000000 0.00000000000000 + x = -0.112814637 + 0.00002026489624 x = -0.112814637 + 0.00002026489624 Combine like terms: -0.112814637 + 0.00002026489624 = -0.11279437210376 x = -0.11279437210376 Simplifying x = -0.11279437210376Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.11283490189624, -0.11279437210376}
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