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Simplifying 16.4 + -2.98722083x = 4.9x2 Solving 16.4 + -2.98722083x = 4.9x2 Solving for variable 'x'. Combine like terms: 4.9x2 + -4.9x2 = 0.0 16.4 + -2.98722083x + -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'. -3.346938776 + 0.6096369041x + x2 = 0 Move the constant term to the right: Add '3.346938776' to each side of the equation. -3.346938776 + 0.6096369041x + 3.346938776 + x2 = 0 + 3.346938776 Reorder the terms: -3.346938776 + 3.346938776 + 0.6096369041x + x2 = 0 + 3.346938776 Combine like terms: -3.346938776 + 3.346938776 = 0.000000000 0.000000000 + 0.6096369041x + x2 = 0 + 3.346938776 0.6096369041x + x2 = 0 + 3.346938776 Combine like terms: 0 + 3.346938776 = 3.346938776 0.6096369041x + x2 = 3.346938776 The x term is 0.6096369041x. Take half its coefficient (0.3048184521). Square it (0.09291428874) and add it to both sides. Add '0.09291428874' to each side of the equation. 0.6096369041x + 0.09291428874 + x2 = 3.346938776 + 0.09291428874 Reorder the terms: 0.09291428874 + 0.6096369041x + x2 = 3.346938776 + 0.09291428874 Combine like terms: 3.346938776 + 0.09291428874 = 3.43985306474 0.09291428874 + 0.6096369041x + x2 = 3.43985306474 Factor a perfect square on the left side: (x + 0.3048184521)(x + 0.3048184521) = 3.43985306474 Calculate the square root of the right side: 1.854684088 Break this problem into two subproblems by setting (x + 0.3048184521) equal to 1.854684088 and -1.854684088.Subproblem 1
x + 0.3048184521 = 1.854684088 Simplifying x + 0.3048184521 = 1.854684088 Reorder the terms: 0.3048184521 + x = 1.854684088 Solving 0.3048184521 + x = 1.854684088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3048184521' to each side of the equation. 0.3048184521 + -0.3048184521 + x = 1.854684088 + -0.3048184521 Combine like terms: 0.3048184521 + -0.3048184521 = 0.0000000000 0.0000000000 + x = 1.854684088 + -0.3048184521 x = 1.854684088 + -0.3048184521 Combine like terms: 1.854684088 + -0.3048184521 = 1.5498656359 x = 1.5498656359 Simplifying x = 1.5498656359Subproblem 2
x + 0.3048184521 = -1.854684088 Simplifying x + 0.3048184521 = -1.854684088 Reorder the terms: 0.3048184521 + x = -1.854684088 Solving 0.3048184521 + x = -1.854684088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3048184521' to each side of the equation. 0.3048184521 + -0.3048184521 + x = -1.854684088 + -0.3048184521 Combine like terms: 0.3048184521 + -0.3048184521 = 0.0000000000 0.0000000000 + x = -1.854684088 + -0.3048184521 x = -1.854684088 + -0.3048184521 Combine like terms: -1.854684088 + -0.3048184521 = -2.1595025401 x = -2.1595025401 Simplifying x = -2.1595025401Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5498656359, -2.1595025401}
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