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Simplifying 0.012x2 + -0.593x + -14.238 = 0 Reorder the terms: -14.238 + -0.593x + 0.012x2 = 0 Solving -14.238 + -0.593x + 0.012x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.012 the coefficient of the squared term: Divide each side by '0.012'. -1186.5 + -49.41666667x + x2 = 0 Move the constant term to the right: Add '1186.5' to each side of the equation. -1186.5 + -49.41666667x + 1186.5 + x2 = 0 + 1186.5 Reorder the terms: -1186.5 + 1186.5 + -49.41666667x + x2 = 0 + 1186.5 Combine like terms: -1186.5 + 1186.5 = 0.0 0.0 + -49.41666667x + x2 = 0 + 1186.5 -49.41666667x + x2 = 0 + 1186.5 Combine like terms: 0 + 1186.5 = 1186.5 -49.41666667x + x2 = 1186.5 The x term is -49.41666667x. Take half its coefficient (-24.70833334). Square it (610.5017364) and add it to both sides. Add '610.5017364' to each side of the equation. -49.41666667x + 610.5017364 + x2 = 1186.5 + 610.5017364 Reorder the terms: 610.5017364 + -49.41666667x + x2 = 1186.5 + 610.5017364 Combine like terms: 1186.5 + 610.5017364 = 1797.0017364 610.5017364 + -49.41666667x + x2 = 1797.0017364 Factor a perfect square on the left side: (x + -24.70833334)(x + -24.70833334) = 1797.0017364 Calculate the square root of the right side: 42.391057269 Break this problem into two subproblems by setting (x + -24.70833334) equal to 42.391057269 and -42.391057269.Subproblem 1
x + -24.70833334 = 42.391057269 Simplifying x + -24.70833334 = 42.391057269 Reorder the terms: -24.70833334 + x = 42.391057269 Solving -24.70833334 + x = 42.391057269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.70833334' to each side of the equation. -24.70833334 + 24.70833334 + x = 42.391057269 + 24.70833334 Combine like terms: -24.70833334 + 24.70833334 = 0.00000000 0.00000000 + x = 42.391057269 + 24.70833334 x = 42.391057269 + 24.70833334 Combine like terms: 42.391057269 + 24.70833334 = 67.099390609 x = 67.099390609 Simplifying x = 67.099390609Subproblem 2
x + -24.70833334 = -42.391057269 Simplifying x + -24.70833334 = -42.391057269 Reorder the terms: -24.70833334 + x = -42.391057269 Solving -24.70833334 + x = -42.391057269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.70833334' to each side of the equation. -24.70833334 + 24.70833334 + x = -42.391057269 + 24.70833334 Combine like terms: -24.70833334 + 24.70833334 = 0.00000000 0.00000000 + x = -42.391057269 + 24.70833334 x = -42.391057269 + 24.70833334 Combine like terms: -42.391057269 + 24.70833334 = -17.682723929 x = -17.682723929 Simplifying x = -17.682723929Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.099390609, -17.682723929}
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