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Simplifying 2x * x + 3x + -203238 = 0 Multiply x * x 2x2 + 3x + -203238 = 0 Reorder the terms: -203238 + 3x + 2x2 = 0 Solving -203238 + 3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -101619 + 1.5x + x2 = 0 Move the constant term to the right: Add '101619' to each side of the equation. -101619 + 1.5x + 101619 + x2 = 0 + 101619 Reorder the terms: -101619 + 101619 + 1.5x + x2 = 0 + 101619 Combine like terms: -101619 + 101619 = 0 0 + 1.5x + x2 = 0 + 101619 1.5x + x2 = 0 + 101619 Combine like terms: 0 + 101619 = 101619 1.5x + x2 = 101619 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 101619 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 101619 + 0.5625 Combine like terms: 101619 + 0.5625 = 101619.5625 0.5625 + 1.5x + x2 = 101619.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 101619.5625 Calculate the square root of the right side: 318.778234044 Break this problem into two subproblems by setting (x + 0.75) equal to 318.778234044 and -318.778234044.Subproblem 1
x + 0.75 = 318.778234044 Simplifying x + 0.75 = 318.778234044 Reorder the terms: 0.75 + x = 318.778234044 Solving 0.75 + x = 318.778234044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 318.778234044 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 318.778234044 + -0.75 x = 318.778234044 + -0.75 Combine like terms: 318.778234044 + -0.75 = 318.028234044 x = 318.028234044 Simplifying x = 318.028234044Subproblem 2
x + 0.75 = -318.778234044 Simplifying x + 0.75 = -318.778234044 Reorder the terms: 0.75 + x = -318.778234044 Solving 0.75 + x = -318.778234044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -318.778234044 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -318.778234044 + -0.75 x = -318.778234044 + -0.75 Combine like terms: -318.778234044 + -0.75 = -319.528234044 x = -319.528234044 Simplifying x = -319.528234044Solution
The solution to the problem is based on the solutions from the subproblems. x = {318.028234044, -319.528234044}
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