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Simplifying (5x + 3) * 3x = 2 Reorder the terms: (3 + 5x) * 3x = 2 Reorder the terms for easier multiplication: 3x(3 + 5x) = 2 (3 * 3x + 5x * 3x) = 2 (9x + 15x2) = 2 Solving 9x + 15x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 9x + 15x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 9x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.1333333333 + 0.6x + x2 = 0 Move the constant term to the right: Add '0.1333333333' to each side of the equation. -0.1333333333 + 0.6x + 0.1333333333 + x2 = 0 + 0.1333333333 Reorder the terms: -0.1333333333 + 0.1333333333 + 0.6x + x2 = 0 + 0.1333333333 Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000 0.0000000000 + 0.6x + x2 = 0 + 0.1333333333 0.6x + x2 = 0 + 0.1333333333 Combine like terms: 0 + 0.1333333333 = 0.1333333333 0.6x + x2 = 0.1333333333 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 0.1333333333 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.1333333333 + 0.09 Combine like terms: 0.1333333333 + 0.09 = 0.2233333333 0.09 + 0.6x + x2 = 0.2233333333 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.2233333333 Calculate the square root of the right side: 0.472581563 Break this problem into two subproblems by setting (x + 0.3) equal to 0.472581563 and -0.472581563.Subproblem 1
x + 0.3 = 0.472581563 Simplifying x + 0.3 = 0.472581563 Reorder the terms: 0.3 + x = 0.472581563 Solving 0.3 + x = 0.472581563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.472581563 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.472581563 + -0.3 x = 0.472581563 + -0.3 Combine like terms: 0.472581563 + -0.3 = 0.172581563 x = 0.172581563 Simplifying x = 0.172581563Subproblem 2
x + 0.3 = -0.472581563 Simplifying x + 0.3 = -0.472581563 Reorder the terms: 0.3 + x = -0.472581563 Solving 0.3 + x = -0.472581563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -0.472581563 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.472581563 + -0.3 x = -0.472581563 + -0.3 Combine like terms: -0.472581563 + -0.3 = -0.772581563 x = -0.772581563 Simplifying x = -0.772581563Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.172581563, -0.772581563}
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