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Simplifying 100x2 + 113.98x + -39893 = 0 Reorder the terms: -39893 + 113.98x + 100x2 = 0 Solving -39893 + 113.98x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -398.93 + 1.1398x + x2 = 0 Move the constant term to the right: Add '398.93' to each side of the equation. -398.93 + 1.1398x + 398.93 + x2 = 0 + 398.93 Reorder the terms: -398.93 + 398.93 + 1.1398x + x2 = 0 + 398.93 Combine like terms: -398.93 + 398.93 = 0.00 0.00 + 1.1398x + x2 = 0 + 398.93 1.1398x + x2 = 0 + 398.93 Combine like terms: 0 + 398.93 = 398.93 1.1398x + x2 = 398.93 The x term is 1.1398x. Take half its coefficient (0.5699). Square it (0.32478601) and add it to both sides. Add '0.32478601' to each side of the equation. 1.1398x + 0.32478601 + x2 = 398.93 + 0.32478601 Reorder the terms: 0.32478601 + 1.1398x + x2 = 398.93 + 0.32478601 Combine like terms: 398.93 + 0.32478601 = 399.25478601 0.32478601 + 1.1398x + x2 = 399.25478601 Factor a perfect square on the left side: (x + 0.5699)(x + 0.5699) = 399.25478601 Calculate the square root of the right side: 19.981360965 Break this problem into two subproblems by setting (x + 0.5699) equal to 19.981360965 and -19.981360965.Subproblem 1
x + 0.5699 = 19.981360965 Simplifying x + 0.5699 = 19.981360965 Reorder the terms: 0.5699 + x = 19.981360965 Solving 0.5699 + x = 19.981360965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5699' to each side of the equation. 0.5699 + -0.5699 + x = 19.981360965 + -0.5699 Combine like terms: 0.5699 + -0.5699 = 0.0000 0.0000 + x = 19.981360965 + -0.5699 x = 19.981360965 + -0.5699 Combine like terms: 19.981360965 + -0.5699 = 19.411460965 x = 19.411460965 Simplifying x = 19.411460965Subproblem 2
x + 0.5699 = -19.981360965 Simplifying x + 0.5699 = -19.981360965 Reorder the terms: 0.5699 + x = -19.981360965 Solving 0.5699 + x = -19.981360965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5699' to each side of the equation. 0.5699 + -0.5699 + x = -19.981360965 + -0.5699 Combine like terms: 0.5699 + -0.5699 = 0.0000 0.0000 + x = -19.981360965 + -0.5699 x = -19.981360965 + -0.5699 Combine like terms: -19.981360965 + -0.5699 = -20.551260965 x = -20.551260965 Simplifying x = -20.551260965Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.411460965, -20.551260965}
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