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Simplifying 5x(x + 3) = 8 Reorder the terms: 5x(3 + x) = 8 (3 * 5x + x * 5x) = 8 (15x + 5x2) = 8 Solving 15x + 5x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 15x + 5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 3x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 3x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 3x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 3x + x2 = 0 + 1.6 3x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 3x + x2 = 1.6 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 = 1.6 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1.6 + 2.25 Combine like terms: 1.6 + 2.25 = 3.85 2.25 + 3x + x2 = 3.85 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.85 Calculate the square root of the right side: 1.962141687 Break this problem into two subproblems by setting (x + 1.5) equal to 1.962141687 and -1.962141687.Subproblem 1
x + 1.5 = 1.962141687 Simplifying x + 1.5 = 1.962141687 Reorder the terms: 1.5 + x = 1.962141687 Solving 1.5 + x = 1.962141687 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 = 1.962141687 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.962141687 + -1.5 x = 1.962141687 + -1.5 Combine like terms: 1.962141687 + -1.5 = 0.462141687 x = 0.462141687 Simplifying x = 0.462141687Subproblem 2
x + 1.5 = -1.962141687 Simplifying x + 1.5 = -1.962141687 Reorder the terms: 1.5 + x = -1.962141687 Solving 1.5 + x = -1.962141687 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 = -1.962141687 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.962141687 + -1.5 x = -1.962141687 + -1.5 Combine like terms: -1.962141687 + -1.5 = -3.462141687 x = -3.462141687 Simplifying x = -3.462141687Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.462141687, -3.462141687}
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