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Simplifying 3x2 + -30x = 4x2 + -3x + -18 Reorder the terms: -30x + 3x2 = 4x2 + -3x + -18 Reorder the terms: -30x + 3x2 = -18 + -3x + 4x2 Solving -30x + 3x2 = -18 + -3x + 4x2 Solving for variable 'x'. Reorder the terms: 18 + -30x + 3x + 3x2 + -4x2 = -18 + -3x + 4x2 + 18 + 3x + -4x2 Combine like terms: -30x + 3x = -27x 18 + -27x + 3x2 + -4x2 = -18 + -3x + 4x2 + 18 + 3x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 18 + -27x + -1x2 = -18 + -3x + 4x2 + 18 + 3x + -4x2 Reorder the terms: 18 + -27x + -1x2 = -18 + 18 + -3x + 3x + 4x2 + -4x2 Combine like terms: -18 + 18 = 0 18 + -27x + -1x2 = 0 + -3x + 3x + 4x2 + -4x2 18 + -27x + -1x2 = -3x + 3x + 4x2 + -4x2 Combine like terms: -3x + 3x = 0 18 + -27x + -1x2 = 0 + 4x2 + -4x2 18 + -27x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 18 + -27x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + 27x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 27x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 27x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 27x + x2 = 0 + 18 27x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 27x + x2 = 18 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = 18 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 18 + 182.25 Combine like terms: 18 + 182.25 = 200.25 182.25 + 27x + x2 = 200.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (x + 13.5) equal to 14.150971698 and -14.150971698.Subproblem 1
x + 13.5 = 14.150971698 Simplifying x + 13.5 = 14.150971698 Reorder the terms: 13.5 + x = 14.150971698 Solving 13.5 + x = 14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 14.150971698 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 14.150971698 + -13.5 x = 14.150971698 + -13.5 Combine like terms: 14.150971698 + -13.5 = 0.650971698 x = 0.650971698 Simplifying x = 0.650971698Subproblem 2
x + 13.5 = -14.150971698 Simplifying x + 13.5 = -14.150971698 Reorder the terms: 13.5 + x = -14.150971698 Solving 13.5 + x = -14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -14.150971698 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -14.150971698 + -13.5 x = -14.150971698 + -13.5 Combine like terms: -14.150971698 + -13.5 = -27.650971698 x = -27.650971698 Simplifying x = -27.650971698Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.650971698, -27.650971698}
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