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Simplifying 0.0003x2 + 2x + 300 = 0 Reorder the terms: 300 + 2x + 0.0003x2 = 0 Solving 300 + 2x + 0.0003x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0003 the coefficient of the squared term: Divide each side by '0.0003'. 1000000 + 6666.666667x + x2 = 0 Move the constant term to the right: Add '-1000000' to each side of the equation. 1000000 + 6666.666667x + -1000000 + x2 = 0 + -1000000 Reorder the terms: 1000000 + -1000000 + 6666.666667x + x2 = 0 + -1000000 Combine like terms: 1000000 + -1000000 = 0 0 + 6666.666667x + x2 = 0 + -1000000 6666.666667x + x2 = 0 + -1000000 Combine like terms: 0 + -1000000 = -1000000 6666.666667x + x2 = -1000000 The x term is 6666.666667x. Take half its coefficient (3333.333334). Square it (11111111.12) and add it to both sides. Add '11111111.12' to each side of the equation. 6666.666667x + 11111111.12 + x2 = -1000000 + 11111111.12 Reorder the terms: 11111111.12 + 6666.666667x + x2 = -1000000 + 11111111.12 Combine like terms: -1000000 + 11111111.12 = 10111111.12 11111111.12 + 6666.666667x + x2 = 10111111.12 Factor a perfect square on the left side: (x + 3333.333334)(x + 3333.333334) = 10111111.12 Calculate the square root of the right side: 3179.797339454 Break this problem into two subproblems by setting (x + 3333.333334) equal to 3179.797339454 and -3179.797339454.Subproblem 1
x + 3333.333334 = 3179.797339454 Simplifying x + 3333.333334 = 3179.797339454 Reorder the terms: 3333.333334 + x = 3179.797339454 Solving 3333.333334 + x = 3179.797339454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3333.333334' to each side of the equation. 3333.333334 + -3333.333334 + x = 3179.797339454 + -3333.333334 Combine like terms: 3333.333334 + -3333.333334 = 0.000000 0.000000 + x = 3179.797339454 + -3333.333334 x = 3179.797339454 + -3333.333334 Combine like terms: 3179.797339454 + -3333.333334 = -153.535994546 x = -153.535994546 Simplifying x = -153.535994546Subproblem 2
x + 3333.333334 = -3179.797339454 Simplifying x + 3333.333334 = -3179.797339454 Reorder the terms: 3333.333334 + x = -3179.797339454 Solving 3333.333334 + x = -3179.797339454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3333.333334' to each side of the equation. 3333.333334 + -3333.333334 + x = -3179.797339454 + -3333.333334 Combine like terms: 3333.333334 + -3333.333334 = 0.000000 0.000000 + x = -3179.797339454 + -3333.333334 x = -3179.797339454 + -3333.333334 Combine like terms: -3179.797339454 + -3333.333334 = -6513.130673454 x = -6513.130673454 Simplifying x = -6513.130673454Solution
The solution to the problem is based on the solutions from the subproblems. x = {-153.535994546, -6513.130673454}
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