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Simplifying 198 = x2 + 3x Reorder the terms: 198 = 3x + x2 Solving 198 = 3x + x2 Solving for variable 'x'. Reorder the terms: 198 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 198 + -3x + -1x2 = 0 + x2 + -1x2 198 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 198 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -198 + 3x + x2 = 0 Move the constant term to the right: Add '198' to each side of the equation. -198 + 3x + 198 + x2 = 0 + 198 Reorder the terms: -198 + 198 + 3x + x2 = 0 + 198 Combine like terms: -198 + 198 = 0 0 + 3x + x2 = 0 + 198 3x + x2 = 0 + 198 Combine like terms: 0 + 198 = 198 3x + x2 = 198 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 198 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 198 + 2.25 Combine like terms: 198 + 2.25 = 200.25 2.25 + 3x + x2 = 200.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (x + 1.5) equal to 14.150971698 and -14.150971698.Subproblem 1
x + 1.5 = 14.150971698 Simplifying x + 1.5 = 14.150971698 Reorder the terms: 1.5 + x = 14.150971698 Solving 1.5 + x = 14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 14.150971698 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.150971698 + -1.5 x = 14.150971698 + -1.5 Combine like terms: 14.150971698 + -1.5 = 12.650971698 x = 12.650971698 Simplifying x = 12.650971698Subproblem 2
x + 1.5 = -14.150971698 Simplifying x + 1.5 = -14.150971698 Reorder the terms: 1.5 + x = -14.150971698 Solving 1.5 + x = -14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -14.150971698 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.150971698 + -1.5 x = -14.150971698 + -1.5 Combine like terms: -14.150971698 + -1.5 = -15.650971698 x = -15.650971698 Simplifying x = -15.650971698Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.650971698, -15.650971698}
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