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Simplifying (x + 3)(5x) + (3x + -2 + -58) = 0 Reorder the terms: (3 + x)(5x) + (3x + -2 + -58) = 0 Remove parenthesis around (5x) (3 + x) * 5x + (3x + -2 + -58) = 0 Reorder the terms for easier multiplication: 5x(3 + x) + (3x + -2 + -58) = 0 (3 * 5x + x * 5x) + (3x + -2 + -58) = 0 (15x + 5x2) + (3x + -2 + -58) = 0 Reorder the terms: 15x + 5x2 + (-2 + -58 + 3x) = 0 Combine like terms: -2 + -58 = -60 15x + 5x2 + (-60 + 3x) = 0 Remove parenthesis around (-60 + 3x) 15x + 5x2 + -60 + 3x = 0 Reorder the terms: -60 + 15x + 3x + 5x2 = 0 Combine like terms: 15x + 3x = 18x -60 + 18x + 5x2 = 0 Solving -60 + 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'. -12 + 3.6x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 3.6x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 3.6x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 3.6x + x2 = 0 + 12 3.6x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 3.6x + x2 = 12 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 = 12 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 12 + 3.24 Combine like terms: 12 + 3.24 = 15.24 3.24 + 3.6x + x2 = 15.24 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 15.24 Calculate the square root of the right side: 3.903844259 Break this problem into two subproblems by setting (x + 1.8) equal to 3.903844259 and -3.903844259.Subproblem 1
x + 1.8 = 3.903844259 Simplifying x + 1.8 = 3.903844259 Reorder the terms: 1.8 + x = 3.903844259 Solving 1.8 + x = 3.903844259 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 = 3.903844259 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 3.903844259 + -1.8 x = 3.903844259 + -1.8 Combine like terms: 3.903844259 + -1.8 = 2.103844259 x = 2.103844259 Simplifying x = 2.103844259Subproblem 2
x + 1.8 = -3.903844259 Simplifying x + 1.8 = -3.903844259 Reorder the terms: 1.8 + x = -3.903844259 Solving 1.8 + x = -3.903844259 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 = -3.903844259 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -3.903844259 + -1.8 x = -3.903844259 + -1.8 Combine like terms: -3.903844259 + -1.8 = -5.703844259 x = -5.703844259 Simplifying x = -5.703844259Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.103844259, -5.703844259}
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