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Simplifying -5x(3x + -4) = -29 + 8x Reorder the terms: -5x(-4 + 3x) = -29 + 8x (-4 * -5x + 3x * -5x) = -29 + 8x (20x + -15x2) = -29 + 8x Solving 20x + -15x2 = -29 + 8x Solving for variable 'x'. Reorder the terms: 29 + 20x + -8x + -15x2 = -29 + 8x + 29 + -8x Combine like terms: 20x + -8x = 12x 29 + 12x + -15x2 = -29 + 8x + 29 + -8x Reorder the terms: 29 + 12x + -15x2 = -29 + 29 + 8x + -8x Combine like terms: -29 + 29 = 0 29 + 12x + -15x2 = 0 + 8x + -8x 29 + 12x + -15x2 = 8x + -8x Combine like terms: 8x + -8x = 0 29 + 12x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -1.933333333 + -0.8x + x2 = 0 Move the constant term to the right: Add '1.933333333' to each side of the equation. -1.933333333 + -0.8x + 1.933333333 + x2 = 0 + 1.933333333 Reorder the terms: -1.933333333 + 1.933333333 + -0.8x + x2 = 0 + 1.933333333 Combine like terms: -1.933333333 + 1.933333333 = 0.000000000 0.000000000 + -0.8x + x2 = 0 + 1.933333333 -0.8x + x2 = 0 + 1.933333333 Combine like terms: 0 + 1.933333333 = 1.933333333 -0.8x + x2 = 1.933333333 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 1.933333333 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 1.933333333 + 0.16 Combine like terms: 1.933333333 + 0.16 = 2.093333333 0.16 + -0.8x + x2 = 2.093333333 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 2.093333333 Calculate the square root of the right side: 1.446835627 Break this problem into two subproblems by setting (x + -0.4) equal to 1.446835627 and -1.446835627.Subproblem 1
x + -0.4 = 1.446835627 Simplifying x + -0.4 = 1.446835627 Reorder the terms: -0.4 + x = 1.446835627 Solving -0.4 + x = 1.446835627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.446835627 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.446835627 + 0.4 x = 1.446835627 + 0.4 Combine like terms: 1.446835627 + 0.4 = 1.846835627 x = 1.846835627 Simplifying x = 1.846835627Subproblem 2
x + -0.4 = -1.446835627 Simplifying x + -0.4 = -1.446835627 Reorder the terms: -0.4 + x = -1.446835627 Solving -0.4 + x = -1.446835627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.446835627 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.446835627 + 0.4 x = -1.446835627 + 0.4 Combine like terms: -1.446835627 + 0.4 = -1.046835627 x = -1.046835627 Simplifying x = -1.046835627Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.846835627, -1.046835627}
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