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Simplifying 98 = 27x + 4.9x2 Solving 98 = 27x + 4.9x2 Solving for variable 'x'. Reorder the terms: 98 + -27x + -4.9x2 = 27x + -27x + 4.9x2 + -4.9x2 Combine like terms: 27x + -27x = 0 98 + -27x + -4.9x2 = 0 + 4.9x2 + -4.9x2 98 + -27x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 98 + -27x + -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'. -20 + 5.510204082x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 5.510204082x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 5.510204082x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 5.510204082x + x2 = 0 + 20 5.510204082x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 5.510204082x + x2 = 20 The x term is 5.510204082x. Take half its coefficient (2.755102041). Square it (7.590587256) and add it to both sides. Add '7.590587256' to each side of the equation. 5.510204082x + 7.590587256 + x2 = 20 + 7.590587256 Reorder the terms: 7.590587256 + 5.510204082x + x2 = 20 + 7.590587256 Combine like terms: 20 + 7.590587256 = 27.590587256 7.590587256 + 5.510204082x + x2 = 27.590587256 Factor a perfect square on the left side: (x + 2.755102041)(x + 2.755102041) = 27.590587256 Calculate the square root of the right side: 5.252674296 Break this problem into two subproblems by setting (x + 2.755102041) equal to 5.252674296 and -5.252674296.Subproblem 1
x + 2.755102041 = 5.252674296 Simplifying x + 2.755102041 = 5.252674296 Reorder the terms: 2.755102041 + x = 5.252674296 Solving 2.755102041 + x = 5.252674296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.755102041' to each side of the equation. 2.755102041 + -2.755102041 + x = 5.252674296 + -2.755102041 Combine like terms: 2.755102041 + -2.755102041 = 0.000000000 0.000000000 + x = 5.252674296 + -2.755102041 x = 5.252674296 + -2.755102041 Combine like terms: 5.252674296 + -2.755102041 = 2.497572255 x = 2.497572255 Simplifying x = 2.497572255Subproblem 2
x + 2.755102041 = -5.252674296 Simplifying x + 2.755102041 = -5.252674296 Reorder the terms: 2.755102041 + x = -5.252674296 Solving 2.755102041 + x = -5.252674296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.755102041' to each side of the equation. 2.755102041 + -2.755102041 + x = -5.252674296 + -2.755102041 Combine like terms: 2.755102041 + -2.755102041 = 0.000000000 0.000000000 + x = -5.252674296 + -2.755102041 x = -5.252674296 + -2.755102041 Combine like terms: -5.252674296 + -2.755102041 = -8.007776337 x = -8.007776337 Simplifying x = -8.007776337Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.497572255, -8.007776337}
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