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Simplifying -2.02x2 + 77.89x + 1279647 = 0 Reorder the terms: 1279647 + 77.89x + -2.02x2 = 0 Solving 1279647 + 77.89x + -2.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.02 the coefficient of the squared term: Divide each side by '-2.02'. -633488.6139 + -38.55940594x + x2 = 0 Move the constant term to the right: Add '633488.6139' to each side of the equation. -633488.6139 + -38.55940594x + 633488.6139 + x2 = 0 + 633488.6139 Reorder the terms: -633488.6139 + 633488.6139 + -38.55940594x + x2 = 0 + 633488.6139 Combine like terms: -633488.6139 + 633488.6139 = 0.0000 0.0000 + -38.55940594x + x2 = 0 + 633488.6139 -38.55940594x + x2 = 0 + 633488.6139 Combine like terms: 0 + 633488.6139 = 633488.6139 -38.55940594x + x2 = 633488.6139 The x term is -38.55940594x. Take half its coefficient (-19.27970297). Square it (371.7069466) and add it to both sides. Add '371.7069466' to each side of the equation. -38.55940594x + 371.7069466 + x2 = 633488.6139 + 371.7069466 Reorder the terms: 371.7069466 + -38.55940594x + x2 = 633488.6139 + 371.7069466 Combine like terms: 633488.6139 + 371.7069466 = 633860.3208466 371.7069466 + -38.55940594x + x2 = 633860.3208466 Factor a perfect square on the left side: (x + -19.27970297)(x + -19.27970297) = 633860.3208466 Calculate the square root of the right side: 796.153453077 Break this problem into two subproblems by setting (x + -19.27970297) equal to 796.153453077 and -796.153453077.Subproblem 1
x + -19.27970297 = 796.153453077 Simplifying x + -19.27970297 = 796.153453077 Reorder the terms: -19.27970297 + x = 796.153453077 Solving -19.27970297 + x = 796.153453077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.27970297' to each side of the equation. -19.27970297 + 19.27970297 + x = 796.153453077 + 19.27970297 Combine like terms: -19.27970297 + 19.27970297 = 0.00000000 0.00000000 + x = 796.153453077 + 19.27970297 x = 796.153453077 + 19.27970297 Combine like terms: 796.153453077 + 19.27970297 = 815.433156047 x = 815.433156047 Simplifying x = 815.433156047Subproblem 2
x + -19.27970297 = -796.153453077 Simplifying x + -19.27970297 = -796.153453077 Reorder the terms: -19.27970297 + x = -796.153453077 Solving -19.27970297 + x = -796.153453077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.27970297' to each side of the equation. -19.27970297 + 19.27970297 + x = -796.153453077 + 19.27970297 Combine like terms: -19.27970297 + 19.27970297 = 0.00000000 0.00000000 + x = -796.153453077 + 19.27970297 x = -796.153453077 + 19.27970297 Combine like terms: -796.153453077 + 19.27970297 = -776.873750107 x = -776.873750107 Simplifying x = -776.873750107Solution
The solution to the problem is based on the solutions from the subproblems. x = {815.433156047, -776.873750107}
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