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Simplifying -8.9x = (4.905(x2)) + -30 Reorder the terms: -8.9x = -30 + (4.905x2) Solving -8.9x = -30 + (4.905x2) Solving for variable 'x'. Reorder the terms: 30 + -8.9x + (-4.905x2) = -30 + (4.905x2) + 30 + (-4.905x2) Reorder the terms: 30 + -8.9x + (-4.905x2) = -30 + 30 + (4.905x2) + (-4.905x2) Combine like terms: -30 + 30 = 0 30 + -8.9x + (-4.905x2) = 0 + (4.905x2) + (-4.905x2) 30 + -8.9x + (-4.905x2) = (4.905x2) + (-4.905x2) Combine like terms: (4.905x2) + (-4.905x2) = 0.000 30 + -8.9x + (-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'. -6.116207951 + 1.814475025x + x2 = 0 Move the constant term to the right: Add '6.116207951' to each side of the equation. -6.116207951 + 1.814475025x + 6.116207951 + x2 = 0 + 6.116207951 Reorder the terms: -6.116207951 + 6.116207951 + 1.814475025x + x2 = 0 + 6.116207951 Combine like terms: -6.116207951 + 6.116207951 = 0.000000000 0.000000000 + 1.814475025x + x2 = 0 + 6.116207951 1.814475025x + x2 = 0 + 6.116207951 Combine like terms: 0 + 6.116207951 = 6.116207951 1.814475025x + x2 = 6.116207951 The x term is 1.814475025x. Take half its coefficient (0.9072375125). Square it (0.8230799041) and add it to both sides. Add '0.8230799041' to each side of the equation. 1.814475025x + 0.8230799041 + x2 = 6.116207951 + 0.8230799041 Reorder the terms: 0.8230799041 + 1.814475025x + x2 = 6.116207951 + 0.8230799041 Combine like terms: 6.116207951 + 0.8230799041 = 6.9392878551 0.8230799041 + 1.814475025x + x2 = 6.9392878551 Factor a perfect square on the left side: ((x) + 0.9072375125)((x) + 0.9072375125) = 6.9392878551 Calculate the square root of the right side: 2.634252808 Break this problem into two subproblems by setting ((x) + 0.9072375125) equal to 2.634252808 and -2.634252808.Subproblem 1
(x) + 0.9072375125 = 2.634252808 Simplifying (x) + 0.9072375125 = 2.634252808 x + 0.9072375125 = 2.634252808 Reorder the terms: 0.9072375125 + x = 2.634252808 Solving 0.9072375125 + x = 2.634252808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9072375125' to each side of the equation. 0.9072375125 + -0.9072375125 + x = 2.634252808 + -0.9072375125 Combine like terms: 0.9072375125 + -0.9072375125 = 0.0000000000 0.0000000000 + x = 2.634252808 + -0.9072375125 x = 2.634252808 + -0.9072375125 Combine like terms: 2.634252808 + -0.9072375125 = 1.7270152955 x = 1.7270152955 Simplifying x = 1.7270152955Subproblem 2
(x) + 0.9072375125 = -2.634252808 Simplifying (x) + 0.9072375125 = -2.634252808 x + 0.9072375125 = -2.634252808 Reorder the terms: 0.9072375125 + x = -2.634252808 Solving 0.9072375125 + x = -2.634252808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9072375125' to each side of the equation. 0.9072375125 + -0.9072375125 + x = -2.634252808 + -0.9072375125 Combine like terms: 0.9072375125 + -0.9072375125 = 0.0000000000 0.0000000000 + x = -2.634252808 + -0.9072375125 x = -2.634252808 + -0.9072375125 Combine like terms: -2.634252808 + -0.9072375125 = -3.5414903205 x = -3.5414903205 Simplifying x = -3.5414903205Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7270152955, -3.5414903205}
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