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Simplifying 0.1x2 + -3x + -2378 = 0 Reorder the terms: -2378 + -3x + 0.1x2 = 0 Solving -2378 + -3x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -23780 + -30x + x2 = 0 Move the constant term to the right: Add '23780' to each side of the equation. -23780 + -30x + 23780 + x2 = 0 + 23780 Reorder the terms: -23780 + 23780 + -30x + x2 = 0 + 23780 Combine like terms: -23780 + 23780 = 0 0 + -30x + x2 = 0 + 23780 -30x + x2 = 0 + 23780 Combine like terms: 0 + 23780 = 23780 -30x + x2 = 23780 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 23780 + 225 Reorder the terms: 225 + -30x + x2 = 23780 + 225 Combine like terms: 23780 + 225 = 24005 225 + -30x + x2 = 24005 Factor a perfect square on the left side: (x + -15)(x + -15) = 24005 Calculate the square root of the right side: 154.935470439 Break this problem into two subproblems by setting (x + -15) equal to 154.935470439 and -154.935470439.Subproblem 1
x + -15 = 154.935470439 Simplifying x + -15 = 154.935470439 Reorder the terms: -15 + x = 154.935470439 Solving -15 + x = 154.935470439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 154.935470439 + 15 Combine like terms: -15 + 15 = 0 0 + x = 154.935470439 + 15 x = 154.935470439 + 15 Combine like terms: 154.935470439 + 15 = 169.935470439 x = 169.935470439 Simplifying x = 169.935470439Subproblem 2
x + -15 = -154.935470439 Simplifying x + -15 = -154.935470439 Reorder the terms: -15 + x = -154.935470439 Solving -15 + x = -154.935470439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -154.935470439 + 15 Combine like terms: -15 + 15 = 0 0 + x = -154.935470439 + 15 x = -154.935470439 + 15 Combine like terms: -154.935470439 + 15 = -139.935470439 x = -139.935470439 Simplifying x = -139.935470439Solution
The solution to the problem is based on the solutions from the subproblems. x = {169.935470439, -139.935470439}
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