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Simplifying 8 = 30x + -4.9x2 Solving 8 = 30x + -4.9x2 Solving for variable 'x'. Reorder the terms: 8 + -30x + 4.9x2 = 30x + -30x + -4.9x2 + 4.9x2 Combine like terms: 30x + -30x = 0 8 + -30x + 4.9x2 = 0 + -4.9x2 + 4.9x2 8 + -30x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 8 + -30x + 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'. 1.632653061 + -6.12244898x + x2 = 0 Move the constant term to the right: Add '-1.632653061' to each side of the equation. 1.632653061 + -6.12244898x + -1.632653061 + x2 = 0 + -1.632653061 Reorder the terms: 1.632653061 + -1.632653061 + -6.12244898x + x2 = 0 + -1.632653061 Combine like terms: 1.632653061 + -1.632653061 = 0.000000000 0.000000000 + -6.12244898x + x2 = 0 + -1.632653061 -6.12244898x + x2 = 0 + -1.632653061 Combine like terms: 0 + -1.632653061 = -1.632653061 -6.12244898x + x2 = -1.632653061 The x term is -6.12244898x. Take half its coefficient (-3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. -6.12244898x + 9.371095378 + x2 = -1.632653061 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898x + x2 = -1.632653061 + 9.371095378 Combine like terms: -1.632653061 + 9.371095378 = 7.738442317 9.371095378 + -6.12244898x + x2 = 7.738442317 Factor a perfect square on the left side: (x + -3.06122449)(x + -3.06122449) = 7.738442317 Calculate the square root of the right side: 2.781805586 Break this problem into two subproblems by setting (x + -3.06122449) equal to 2.781805586 and -2.781805586.Subproblem 1
x + -3.06122449 = 2.781805586 Simplifying x + -3.06122449 = 2.781805586 Reorder the terms: -3.06122449 + x = 2.781805586 Solving -3.06122449 + x = 2.781805586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + x = 2.781805586 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = 2.781805586 + 3.06122449 x = 2.781805586 + 3.06122449 Combine like terms: 2.781805586 + 3.06122449 = 5.843030076 x = 5.843030076 Simplifying x = 5.843030076Subproblem 2
x + -3.06122449 = -2.781805586 Simplifying x + -3.06122449 = -2.781805586 Reorder the terms: -3.06122449 + x = -2.781805586 Solving -3.06122449 + x = -2.781805586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + x = -2.781805586 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = -2.781805586 + 3.06122449 x = -2.781805586 + 3.06122449 Combine like terms: -2.781805586 + 3.06122449 = 0.279418904 x = 0.279418904 Simplifying x = 0.279418904Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.843030076, 0.279418904}
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