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Simplifying 5x2 + 13x + -18 = 3 + -5x Reorder the terms: -18 + 13x + 5x2 = 3 + -5x Solving -18 + 13x + 5x2 = 3 + -5x Solving for variable 'x'. Reorder the terms: -18 + -3 + 13x + 5x + 5x2 = 3 + -5x + -3 + 5x Combine like terms: -18 + -3 = -21 -21 + 13x + 5x + 5x2 = 3 + -5x + -3 + 5x Combine like terms: 13x + 5x = 18x -21 + 18x + 5x2 = 3 + -5x + -3 + 5x Reorder the terms: -21 + 18x + 5x2 = 3 + -3 + -5x + 5x Combine like terms: 3 + -3 = 0 -21 + 18x + 5x2 = 0 + -5x + 5x -21 + 18x + 5x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -21 + 18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + 3.6x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 3.6x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 3.6x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 3.6x + x2 = 0 + 4.2 3.6x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 3.6x + x2 = 4.2 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 4.2 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 4.2 + 3.24 Combine like terms: 4.2 + 3.24 = 7.44 3.24 + 3.6x + x2 = 7.44 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 7.44 Calculate the square root of the right side: 2.727636339 Break this problem into two subproblems by setting (x + 1.8) equal to 2.727636339 and -2.727636339.Subproblem 1
x + 1.8 = 2.727636339 Simplifying x + 1.8 = 2.727636339 Reorder the terms: 1.8 + x = 2.727636339 Solving 1.8 + x = 2.727636339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 2.727636339 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 2.727636339 + -1.8 x = 2.727636339 + -1.8 Combine like terms: 2.727636339 + -1.8 = 0.927636339 x = 0.927636339 Simplifying x = 0.927636339Subproblem 2
x + 1.8 = -2.727636339 Simplifying x + 1.8 = -2.727636339 Reorder the terms: 1.8 + x = -2.727636339 Solving 1.8 + x = -2.727636339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -2.727636339 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -2.727636339 + -1.8 x = -2.727636339 + -1.8 Combine like terms: -2.727636339 + -1.8 = -4.527636339 x = -4.527636339 Simplifying x = -4.527636339Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.927636339, -4.527636339}
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