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Simplifying 0 = 2 + 15.05x + -4.9x2 Solving 0 = 2 + 15.05x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -15.05x + 4.9x2 = 2 + 15.05x + -4.9x2 + -2 + -15.05x + 4.9x2 Reorder the terms: -2 + -15.05x + 4.9x2 = 2 + -2 + 15.05x + -15.05x + -4.9x2 + 4.9x2 Combine like terms: 2 + -2 = 0 -2 + -15.05x + 4.9x2 = 0 + 15.05x + -15.05x + -4.9x2 + 4.9x2 -2 + -15.05x + 4.9x2 = 15.05x + -15.05x + -4.9x2 + 4.9x2 Combine like terms: 15.05x + -15.05x = 0.00 -2 + -15.05x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 -2 + -15.05x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -2 + -15.05x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.4081632653 + -3.071428571x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -3.071428571x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -3.071428571x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -3.071428571x + x2 = 0 + 0.4081632653 -3.071428571x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -3.071428571x + x2 = 0.4081632653 The x term is -3.071428571x. Take half its coefficient (-1.535714286). Square it (2.358418368) and add it to both sides. Add '2.358418368' to each side of the equation. -3.071428571x + 2.358418368 + x2 = 0.4081632653 + 2.358418368 Reorder the terms: 2.358418368 + -3.071428571x + x2 = 0.4081632653 + 2.358418368 Combine like terms: 0.4081632653 + 2.358418368 = 2.7665816333 2.358418368 + -3.071428571x + x2 = 2.7665816333 Factor a perfect square on the left side: (x + -1.535714286)(x + -1.535714286) = 2.7665816333 Calculate the square root of the right side: 1.663304432 Break this problem into two subproblems by setting (x + -1.535714286) equal to 1.663304432 and -1.663304432.Subproblem 1
x + -1.535714286 = 1.663304432 Simplifying x + -1.535714286 = 1.663304432 Reorder the terms: -1.535714286 + x = 1.663304432 Solving -1.535714286 + x = 1.663304432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.535714286' to each side of the equation. -1.535714286 + 1.535714286 + x = 1.663304432 + 1.535714286 Combine like terms: -1.535714286 + 1.535714286 = 0.000000000 0.000000000 + x = 1.663304432 + 1.535714286 x = 1.663304432 + 1.535714286 Combine like terms: 1.663304432 + 1.535714286 = 3.199018718 x = 3.199018718 Simplifying x = 3.199018718Subproblem 2
x + -1.535714286 = -1.663304432 Simplifying x + -1.535714286 = -1.663304432 Reorder the terms: -1.535714286 + x = -1.663304432 Solving -1.535714286 + x = -1.663304432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.535714286' to each side of the equation. -1.535714286 + 1.535714286 + x = -1.663304432 + 1.535714286 Combine like terms: -1.535714286 + 1.535714286 = 0.000000000 0.000000000 + x = -1.663304432 + 1.535714286 x = -1.663304432 + 1.535714286 Combine like terms: -1.663304432 + 1.535714286 = -0.127590146 x = -0.127590146 Simplifying x = -0.127590146Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.199018718, -0.127590146}
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