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Simplifying 5(2x + -1) * 3x = 5x + 9 Reorder the terms: 5(-1 + 2x) * 3x = 5x + 9 Reorder the terms for easier multiplication: 5 * 3x(-1 + 2x) = 5x + 9 Multiply 5 * 3 15x(-1 + 2x) = 5x + 9 (-1 * 15x + 2x * 15x) = 5x + 9 (-15x + 30x2) = 5x + 9 Reorder the terms: -15x + 30x2 = 9 + 5x Solving -15x + 30x2 = 9 + 5x Solving for variable 'x'. Reorder the terms: -9 + -15x + -5x + 30x2 = 9 + 5x + -9 + -5x Combine like terms: -15x + -5x = -20x -9 + -20x + 30x2 = 9 + 5x + -9 + -5x Reorder the terms: -9 + -20x + 30x2 = 9 + -9 + 5x + -5x Combine like terms: 9 + -9 = 0 -9 + -20x + 30x2 = 0 + 5x + -5x -9 + -20x + 30x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -9 + -20x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.3 + -0.6666666667x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.6666666667x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.6666666667x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.6666666667x + x2 = 0.0 + 0.3 -0.6666666667x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -0.6666666667x + x2 = 0.3 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 0.3 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 0.3 + 0.1111111112 Combine like terms: 0.3 + 0.1111111112 = 0.4111111112 0.1111111112 + -0.6666666667x + x2 = 0.4111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.4111111112 Calculate the square root of the right side: 0.641179469 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.641179469 and -0.641179469.Subproblem 1
x + -0.3333333334 = 0.641179469 Simplifying x + -0.3333333334 = 0.641179469 Reorder the terms: -0.3333333334 + x = 0.641179469 Solving -0.3333333334 + x = 0.641179469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 0.641179469 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.641179469 + 0.3333333334 x = 0.641179469 + 0.3333333334 Combine like terms: 0.641179469 + 0.3333333334 = 0.9745128024 x = 0.9745128024 Simplifying x = 0.9745128024Subproblem 2
x + -0.3333333334 = -0.641179469 Simplifying x + -0.3333333334 = -0.641179469 Reorder the terms: -0.3333333334 + x = -0.641179469 Solving -0.3333333334 + x = -0.641179469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -0.641179469 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.641179469 + 0.3333333334 x = -0.641179469 + 0.3333333334 Combine like terms: -0.641179469 + 0.3333333334 = -0.3078461356 x = -0.3078461356 Simplifying x = -0.3078461356Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9745128024, -0.3078461356}
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