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Simplifying (x + 3)(5x) + (3x + -2 + -5) = 0 Reorder the terms: (3 + x)(5x) + (3x + -2 + -5) = 0 Remove parenthesis around (5x) (3 + x) * 5x + (3x + -2 + -5) = 0 Reorder the terms for easier multiplication: 5x(3 + x) + (3x + -2 + -5) = 0 (3 * 5x + x * 5x) + (3x + -2 + -5) = 0 (15x + 5x2) + (3x + -2 + -5) = 0 Reorder the terms: 15x + 5x2 + (-2 + -5 + 3x) = 0 Combine like terms: -2 + -5 = -7 15x + 5x2 + (-7 + 3x) = 0 Remove parenthesis around (-7 + 3x) 15x + 5x2 + -7 + 3x = 0 Reorder the terms: -7 + 15x + 3x + 5x2 = 0 Combine like terms: 15x + 3x = 18x -7 + 18x + 5x2 = 0 Solving -7 + 18x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 3.6x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 3.6x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 3.6x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 3.6x + x2 = 0 + 1.4 3.6x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 3.6x + x2 = 1.4 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 = 1.4 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 1.4 + 3.24 Combine like terms: 1.4 + 3.24 = 4.64 3.24 + 3.6x + x2 = 4.64 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 4.64 Calculate the square root of the right side: 2.154065923 Break this problem into two subproblems by setting (x + 1.8) equal to 2.154065923 and -2.154065923.Subproblem 1
x + 1.8 = 2.154065923 Simplifying x + 1.8 = 2.154065923 Reorder the terms: 1.8 + x = 2.154065923 Solving 1.8 + x = 2.154065923 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 = 2.154065923 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 2.154065923 + -1.8 x = 2.154065923 + -1.8 Combine like terms: 2.154065923 + -1.8 = 0.354065923 x = 0.354065923 Simplifying x = 0.354065923Subproblem 2
x + 1.8 = -2.154065923 Simplifying x + 1.8 = -2.154065923 Reorder the terms: 1.8 + x = -2.154065923 Solving 1.8 + x = -2.154065923 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 = -2.154065923 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -2.154065923 + -1.8 x = -2.154065923 + -1.8 Combine like terms: -2.154065923 + -1.8 = -3.954065923 x = -3.954065923 Simplifying x = -3.954065923Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.354065923, -3.954065923}
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