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Simplifying x(2x + 3) = 13 + -3x Reorder the terms: x(3 + 2x) = 13 + -3x (3 * x + 2x * x) = 13 + -3x (3x + 2x2) = 13 + -3x Solving 3x + 2x2 = 13 + -3x Solving for variable 'x'. Reorder the terms: -13 + 3x + 3x + 2x2 = 13 + -3x + -13 + 3x Combine like terms: 3x + 3x = 6x -13 + 6x + 2x2 = 13 + -3x + -13 + 3x Reorder the terms: -13 + 6x + 2x2 = 13 + -13 + -3x + 3x Combine like terms: 13 + -13 = 0 -13 + 6x + 2x2 = 0 + -3x + 3x -13 + 6x + 2x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -13 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + 3x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 3x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 3x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 3x + x2 = 0 + 6.5 3x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 3x + x2 = 6.5 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 = 6.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 6.5 + 2.25 Combine like terms: 6.5 + 2.25 = 8.75 2.25 + 3x + x2 = 8.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + 1.5) equal to 2.958039892 and -2.958039892.Subproblem 1
x + 1.5 = 2.958039892 Simplifying x + 1.5 = 2.958039892 Reorder the terms: 1.5 + x = 2.958039892 Solving 1.5 + x = 2.958039892 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 = 2.958039892 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.958039892 + -1.5 x = 2.958039892 + -1.5 Combine like terms: 2.958039892 + -1.5 = 1.458039892 x = 1.458039892 Simplifying x = 1.458039892Subproblem 2
x + 1.5 = -2.958039892 Simplifying x + 1.5 = -2.958039892 Reorder the terms: 1.5 + x = -2.958039892 Solving 1.5 + x = -2.958039892 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 = -2.958039892 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.958039892 + -1.5 x = -2.958039892 + -1.5 Combine like terms: -2.958039892 + -1.5 = -4.458039892 x = -4.458039892 Simplifying x = -4.458039892Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.458039892, -4.458039892}
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