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Simplifying (0.000001805) * x2 + -0.001881x + -0.01 = 0 Reorder the terms: -0.01 + -0.001881x + 0.000001805x2 = 0 Solving -0.01 + -0.001881x + 0.000001805x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.000001805 the coefficient of the squared term: Divide each side by '0.000001805'. -5540.166205 + -1042.105263x + x2 = 0 Move the constant term to the right: Add '5540.166205' to each side of the equation. -5540.166205 + -1042.105263x + 5540.166205 + x2 = 0 + 5540.166205 Reorder the terms: -5540.166205 + 5540.166205 + -1042.105263x + x2 = 0 + 5540.166205 Combine like terms: -5540.166205 + 5540.166205 = 0.000000 0.000000 + -1042.105263x + x2 = 0 + 5540.166205 -1042.105263x + x2 = 0 + 5540.166205 Combine like terms: 0 + 5540.166205 = 5540.166205 -1042.105263x + x2 = 5540.166205 The x term is -1042.105263x. Take half its coefficient (-521.0526315). Square it (271495.8448) and add it to both sides. Add '271495.8448' to each side of the equation. -1042.105263x + 271495.8448 + x2 = 5540.166205 + 271495.8448 Reorder the terms: 271495.8448 + -1042.105263x + x2 = 5540.166205 + 271495.8448 Combine like terms: 5540.166205 + 271495.8448 = 277036.011005 271495.8448 + -1042.105263x + x2 = 277036.011005 Factor a perfect square on the left side: (x + -521.0526315)(x + -521.0526315) = 277036.011005 Calculate the square root of the right side: 526.342104534 Break this problem into two subproblems by setting (x + -521.0526315) equal to 526.342104534 and -526.342104534.Subproblem 1
x + -521.0526315 = 526.342104534 Simplifying x + -521.0526315 = 526.342104534 Reorder the terms: -521.0526315 + x = 526.342104534 Solving -521.0526315 + x = 526.342104534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '521.0526315' to each side of the equation. -521.0526315 + 521.0526315 + x = 526.342104534 + 521.0526315 Combine like terms: -521.0526315 + 521.0526315 = 0.0000000 0.0000000 + x = 526.342104534 + 521.0526315 x = 526.342104534 + 521.0526315 Combine like terms: 526.342104534 + 521.0526315 = 1047.394736034 x = 1047.394736034 Simplifying x = 1047.394736034Subproblem 2
x + -521.0526315 = -526.342104534 Simplifying x + -521.0526315 = -526.342104534 Reorder the terms: -521.0526315 + x = -526.342104534 Solving -521.0526315 + x = -526.342104534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '521.0526315' to each side of the equation. -521.0526315 + 521.0526315 + x = -526.342104534 + 521.0526315 Combine like terms: -521.0526315 + 521.0526315 = 0.0000000 0.0000000 + x = -526.342104534 + 521.0526315 x = -526.342104534 + 521.0526315 Combine like terms: -526.342104534 + 521.0526315 = -5.289473034 x = -5.289473034 Simplifying x = -5.289473034Solution
The solution to the problem is based on the solutions from the subproblems. x = {1047.394736034, -5.289473034}
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