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Simplifying 20.4 = 20x + 0.5(9.81) * x2 Multiply 0.5 * 9.81 20.4 = 20x + 4.905x2 Solving 20.4 = 20x + 4.905x2 Solving for variable 'x'. Reorder the terms: 20.4 + -20x + -4.905x2 = 20x + -20x + 4.905x2 + -4.905x2 Combine like terms: 20x + -20x = 0 20.4 + -20x + -4.905x2 = 0 + 4.905x2 + -4.905x2 20.4 + -20x + -4.905x2 = 4.905x2 + -4.905x2 Combine like terms: 4.905x2 + -4.905x2 = 0.000 20.4 + -20x + -4.905x2 = 0.000 Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -4.159021407 + 4.077471967x + x2 = 0 Move the constant term to the right: Add '4.159021407' to each side of the equation. -4.159021407 + 4.077471967x + 4.159021407 + x2 = 0 + 4.159021407 Reorder the terms: -4.159021407 + 4.159021407 + 4.077471967x + x2 = 0 + 4.159021407 Combine like terms: -4.159021407 + 4.159021407 = 0.000000000 0.000000000 + 4.077471967x + x2 = 0 + 4.159021407 4.077471967x + x2 = 0 + 4.159021407 Combine like terms: 0 + 4.159021407 = 4.159021407 4.077471967x + x2 = 4.159021407 The x term is 4.077471967x. Take half its coefficient (2.038735984). Square it (4.156444412) and add it to both sides. Add '4.156444412' to each side of the equation. 4.077471967x + 4.156444412 + x2 = 4.159021407 + 4.156444412 Reorder the terms: 4.156444412 + 4.077471967x + x2 = 4.159021407 + 4.156444412 Combine like terms: 4.159021407 + 4.156444412 = 8.315465819 4.156444412 + 4.077471967x + x2 = 8.315465819 Factor a perfect square on the left side: (x + 2.038735984)(x + 2.038735984) = 8.315465819 Calculate the square root of the right side: 2.883654941 Break this problem into two subproblems by setting (x + 2.038735984) equal to 2.883654941 and -2.883654941.Subproblem 1
x + 2.038735984 = 2.883654941 Simplifying x + 2.038735984 = 2.883654941 Reorder the terms: 2.038735984 + x = 2.883654941 Solving 2.038735984 + x = 2.883654941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.038735984' to each side of the equation. 2.038735984 + -2.038735984 + x = 2.883654941 + -2.038735984 Combine like terms: 2.038735984 + -2.038735984 = 0.000000000 0.000000000 + x = 2.883654941 + -2.038735984 x = 2.883654941 + -2.038735984 Combine like terms: 2.883654941 + -2.038735984 = 0.844918957 x = 0.844918957 Simplifying x = 0.844918957Subproblem 2
x + 2.038735984 = -2.883654941 Simplifying x + 2.038735984 = -2.883654941 Reorder the terms: 2.038735984 + x = -2.883654941 Solving 2.038735984 + x = -2.883654941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.038735984' to each side of the equation. 2.038735984 + -2.038735984 + x = -2.883654941 + -2.038735984 Combine like terms: 2.038735984 + -2.038735984 = 0.000000000 0.000000000 + x = -2.883654941 + -2.038735984 x = -2.883654941 + -2.038735984 Combine like terms: -2.883654941 + -2.038735984 = -4.922390925 x = -4.922390925 Simplifying x = -4.922390925Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.844918957, -4.922390925}
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