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Simplifying -2.1x2 + 77.9x + -391.8 = 0 Reorder the terms: -391.8 + 77.9x + -2.1x2 = 0 Solving -391.8 + 77.9x + -2.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.1 the coefficient of the squared term: Divide each side by '-2.1'. 186.5714286 + -37.0952381x + x2 = 0 Move the constant term to the right: Add '-186.5714286' to each side of the equation. 186.5714286 + -37.0952381x + -186.5714286 + x2 = 0 + -186.5714286 Reorder the terms: 186.5714286 + -186.5714286 + -37.0952381x + x2 = 0 + -186.5714286 Combine like terms: 186.5714286 + -186.5714286 = 0.0000000 0.0000000 + -37.0952381x + x2 = 0 + -186.5714286 -37.0952381x + x2 = 0 + -186.5714286 Combine like terms: 0 + -186.5714286 = -186.5714286 -37.0952381x + x2 = -186.5714286 The x term is -37.0952381x. Take half its coefficient (-18.54761905). Square it (344.0141724) and add it to both sides. Add '344.0141724' to each side of the equation. -37.0952381x + 344.0141724 + x2 = -186.5714286 + 344.0141724 Reorder the terms: 344.0141724 + -37.0952381x + x2 = -186.5714286 + 344.0141724 Combine like terms: -186.5714286 + 344.0141724 = 157.4427438 344.0141724 + -37.0952381x + x2 = 157.4427438 Factor a perfect square on the left side: (x + -18.54761905)(x + -18.54761905) = 157.4427438 Calculate the square root of the right side: 12.547619049 Break this problem into two subproblems by setting (x + -18.54761905) equal to 12.547619049 and -12.547619049.Subproblem 1
x + -18.54761905 = 12.547619049 Simplifying x + -18.54761905 = 12.547619049 Reorder the terms: -18.54761905 + x = 12.547619049 Solving -18.54761905 + x = 12.547619049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.54761905' to each side of the equation. -18.54761905 + 18.54761905 + x = 12.547619049 + 18.54761905 Combine like terms: -18.54761905 + 18.54761905 = 0.00000000 0.00000000 + x = 12.547619049 + 18.54761905 x = 12.547619049 + 18.54761905 Combine like terms: 12.547619049 + 18.54761905 = 31.095238099 x = 31.095238099 Simplifying x = 31.095238099Subproblem 2
x + -18.54761905 = -12.547619049 Simplifying x + -18.54761905 = -12.547619049 Reorder the terms: -18.54761905 + x = -12.547619049 Solving -18.54761905 + x = -12.547619049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.54761905' to each side of the equation. -18.54761905 + 18.54761905 + x = -12.547619049 + 18.54761905 Combine like terms: -18.54761905 + 18.54761905 = 0.00000000 0.00000000 + x = -12.547619049 + 18.54761905 x = -12.547619049 + 18.54761905 Combine like terms: -12.547619049 + 18.54761905 = 6.000000001 x = 6.000000001 Simplifying x = 6.000000001Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.095238099, 6.000000001}
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