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Simplifying 4.905x2 + -58x + 100 = 0 Reorder the terms: 100 + -58x + 4.905x2 = 0 Solving 100 + -58x + 4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. 20.38735984 + -11.82466871x + x2 = 0 Move the constant term to the right: Add '-20.38735984' to each side of the equation. 20.38735984 + -11.82466871x + -20.38735984 + x2 = 0 + -20.38735984 Reorder the terms: 20.38735984 + -20.38735984 + -11.82466871x + x2 = 0 + -20.38735984 Combine like terms: 20.38735984 + -20.38735984 = 0.00000000 0.00000000 + -11.82466871x + x2 = 0 + -20.38735984 -11.82466871x + x2 = 0 + -20.38735984 Combine like terms: 0 + -20.38735984 = -20.38735984 -11.82466871x + x2 = -20.38735984 The x term is -11.82466871x. Take half its coefficient (-5.912334355). Square it (34.95569753) and add it to both sides. Add '34.95569753' to each side of the equation. -11.82466871x + 34.95569753 + x2 = -20.38735984 + 34.95569753 Reorder the terms: 34.95569753 + -11.82466871x + x2 = -20.38735984 + 34.95569753 Combine like terms: -20.38735984 + 34.95569753 = 14.56833769 34.95569753 + -11.82466871x + x2 = 14.56833769 Factor a perfect square on the left side: (x + -5.912334355)(x + -5.912334355) = 14.56833769 Calculate the square root of the right side: 3.816849184 Break this problem into two subproblems by setting (x + -5.912334355) equal to 3.816849184 and -3.816849184.Subproblem 1
x + -5.912334355 = 3.816849184 Simplifying x + -5.912334355 = 3.816849184 Reorder the terms: -5.912334355 + x = 3.816849184 Solving -5.912334355 + x = 3.816849184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.912334355' to each side of the equation. -5.912334355 + 5.912334355 + x = 3.816849184 + 5.912334355 Combine like terms: -5.912334355 + 5.912334355 = 0.000000000 0.000000000 + x = 3.816849184 + 5.912334355 x = 3.816849184 + 5.912334355 Combine like terms: 3.816849184 + 5.912334355 = 9.729183539 x = 9.729183539 Simplifying x = 9.729183539Subproblem 2
x + -5.912334355 = -3.816849184 Simplifying x + -5.912334355 = -3.816849184 Reorder the terms: -5.912334355 + x = -3.816849184 Solving -5.912334355 + x = -3.816849184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.912334355' to each side of the equation. -5.912334355 + 5.912334355 + x = -3.816849184 + 5.912334355 Combine like terms: -5.912334355 + 5.912334355 = 0.000000000 0.000000000 + x = -3.816849184 + 5.912334355 x = -3.816849184 + 5.912334355 Combine like terms: -3.816849184 + 5.912334355 = 2.095485171 x = 2.095485171 Simplifying x = 2.095485171Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.729183539, 2.095485171}
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