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Simplifying 3x(1 + 5x) = 9 + -1(2x + 7) + -1x (1 * 3x + 5x * 3x) = 9 + -1(2x + 7) + -1x (3x + 15x2) = 9 + -1(2x + 7) + -1x Reorder the terms: 3x + 15x2 = 9 + -1(7 + 2x) + -1x 3x + 15x2 = 9 + (7 * -1 + 2x * -1) + -1x 3x + 15x2 = 9 + (-7 + -2x) + -1x Combine like terms: 9 + -7 = 2 3x + 15x2 = 2 + -2x + -1x Combine like terms: -2x + -1x = -3x 3x + 15x2 = 2 + -3x Solving 3x + 15x2 = 2 + -3x Solving for variable 'x'. Reorder the terms: -2 + 3x + 3x + 15x2 = 2 + -3x + -2 + 3x Combine like terms: 3x + 3x = 6x -2 + 6x + 15x2 = 2 + -3x + -2 + 3x Reorder the terms: -2 + 6x + 15x2 = 2 + -2 + -3x + 3x Combine like terms: 2 + -2 = 0 -2 + 6x + 15x2 = 0 + -3x + 3x -2 + 6x + 15x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -2 + 6x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.1333333333 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.1333333333' to each side of the equation. -0.1333333333 + 0.4x + 0.1333333333 + x2 = 0 + 0.1333333333 Reorder the terms: -0.1333333333 + 0.1333333333 + 0.4x + x2 = 0 + 0.1333333333 Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000 0.0000000000 + 0.4x + x2 = 0 + 0.1333333333 0.4x + x2 = 0 + 0.1333333333 Combine like terms: 0 + 0.1333333333 = 0.1333333333 0.4x + x2 = 0.1333333333 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.1333333333 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.1333333333 + 0.04 Combine like terms: 0.1333333333 + 0.04 = 0.1733333333 0.04 + 0.4x + x2 = 0.1733333333 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.1733333333 Calculate the square root of the right side: 0.4163332 Break this problem into two subproblems by setting (x + 0.2) equal to 0.4163332 and -0.4163332.Subproblem 1
x + 0.2 = 0.4163332 Simplifying x + 0.2 = 0.4163332 Reorder the terms: 0.2 + x = 0.4163332 Solving 0.2 + x = 0.4163332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.4163332 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.4163332 + -0.2 x = 0.4163332 + -0.2 Combine like terms: 0.4163332 + -0.2 = 0.2163332 x = 0.2163332 Simplifying x = 0.2163332Subproblem 2
x + 0.2 = -0.4163332 Simplifying x + 0.2 = -0.4163332 Reorder the terms: 0.2 + x = -0.4163332 Solving 0.2 + x = -0.4163332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.4163332 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.4163332 + -0.2 x = -0.4163332 + -0.2 Combine like terms: -0.4163332 + -0.2 = -0.6163332 x = -0.6163332 Simplifying x = -0.6163332Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2163332, -0.6163332}
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