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Simplifying 0 = 305 + 86x + -4.9x2 Solving 0 = 305 + 86x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -305 = -305 -305 + -86x + 4.9x2 = 305 + 86x + -4.9x2 + -305 + -86x + 4.9x2 Reorder the terms: -305 + -86x + 4.9x2 = 305 + -305 + 86x + -86x + -4.9x2 + 4.9x2 Combine like terms: 305 + -305 = 0 -305 + -86x + 4.9x2 = 0 + 86x + -86x + -4.9x2 + 4.9x2 -305 + -86x + 4.9x2 = 86x + -86x + -4.9x2 + 4.9x2 Combine like terms: 86x + -86x = 0 -305 + -86x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -305 + -86x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -305 + -86x + 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'. -62.24489796 + -17.55102041x + x2 = 0 Move the constant term to the right: Add '62.24489796' to each side of the equation. -62.24489796 + -17.55102041x + 62.24489796 + x2 = 0 + 62.24489796 Reorder the terms: -62.24489796 + 62.24489796 + -17.55102041x + x2 = 0 + 62.24489796 Combine like terms: -62.24489796 + 62.24489796 = 0.00000000 0.00000000 + -17.55102041x + x2 = 0 + 62.24489796 -17.55102041x + x2 = 0 + 62.24489796 Combine like terms: 0 + 62.24489796 = 62.24489796 -17.55102041x + x2 = 62.24489796 The x term is -17.55102041x. Take half its coefficient (-8.775510205). Square it (77.00957936) and add it to both sides. Add '77.00957936' to each side of the equation. -17.55102041x + 77.00957936 + x2 = 62.24489796 + 77.00957936 Reorder the terms: 77.00957936 + -17.55102041x + x2 = 62.24489796 + 77.00957936 Combine like terms: 62.24489796 + 77.00957936 = 139.25447732 77.00957936 + -17.55102041x + x2 = 139.25447732 Factor a perfect square on the left side: (x + -8.775510205)(x + -8.775510205) = 139.25447732 Calculate the square root of the right side: 11.80061343 Break this problem into two subproblems by setting (x + -8.775510205) equal to 11.80061343 and -11.80061343.Subproblem 1
x + -8.775510205 = 11.80061343 Simplifying x + -8.775510205 = 11.80061343 Reorder the terms: -8.775510205 + x = 11.80061343 Solving -8.775510205 + x = 11.80061343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.775510205' to each side of the equation. -8.775510205 + 8.775510205 + x = 11.80061343 + 8.775510205 Combine like terms: -8.775510205 + 8.775510205 = 0.000000000 0.000000000 + x = 11.80061343 + 8.775510205 x = 11.80061343 + 8.775510205 Combine like terms: 11.80061343 + 8.775510205 = 20.576123635 x = 20.576123635 Simplifying x = 20.576123635Subproblem 2
x + -8.775510205 = -11.80061343 Simplifying x + -8.775510205 = -11.80061343 Reorder the terms: -8.775510205 + x = -11.80061343 Solving -8.775510205 + x = -11.80061343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.775510205' to each side of the equation. -8.775510205 + 8.775510205 + x = -11.80061343 + 8.775510205 Combine like terms: -8.775510205 + 8.775510205 = 0.000000000 0.000000000 + x = -11.80061343 + 8.775510205 x = -11.80061343 + 8.775510205 Combine like terms: -11.80061343 + 8.775510205 = -3.025103225 x = -3.025103225 Simplifying x = -3.025103225Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.576123635, -3.025103225}
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