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Simplifying 3x + -8x(2x + 3) = -6(2x + 5) Reorder the terms: 3x + -8x(3 + 2x) = -6(2x + 5) 3x + (3 * -8x + 2x * -8x) = -6(2x + 5) 3x + (-24x + -16x2) = -6(2x + 5) Combine like terms: 3x + -24x = -21x -21x + -16x2 = -6(2x + 5) Reorder the terms: -21x + -16x2 = -6(5 + 2x) -21x + -16x2 = (5 * -6 + 2x * -6) -21x + -16x2 = (-30 + -12x) Solving -21x + -16x2 = -30 + -12x Solving for variable 'x'. Reorder the terms: 30 + -21x + 12x + -16x2 = -30 + -12x + 30 + 12x Combine like terms: -21x + 12x = -9x 30 + -9x + -16x2 = -30 + -12x + 30 + 12x Reorder the terms: 30 + -9x + -16x2 = -30 + 30 + -12x + 12x Combine like terms: -30 + 30 = 0 30 + -9x + -16x2 = 0 + -12x + 12x 30 + -9x + -16x2 = -12x + 12x Combine like terms: -12x + 12x = 0 30 + -9x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.875 + 0.5625x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 0.5625x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 0.5625x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 0.5625x + x2 = 0 + 1.875 0.5625x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 0.5625x + x2 = 1.875 The x term is 0.5625x. Take half its coefficient (0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. 0.5625x + 0.0791015625 + x2 = 1.875 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625x + x2 = 1.875 + 0.0791015625 Combine like terms: 1.875 + 0.0791015625 = 1.9541015625 0.0791015625 + 0.5625x + x2 = 1.9541015625 Factor a perfect square on the left side: (x + 0.28125)(x + 0.28125) = 1.9541015625 Calculate the square root of the right side: 1.397891828 Break this problem into two subproblems by setting (x + 0.28125) equal to 1.397891828 and -1.397891828.Subproblem 1
x + 0.28125 = 1.397891828 Simplifying x + 0.28125 = 1.397891828 Reorder the terms: 0.28125 + x = 1.397891828 Solving 0.28125 + x = 1.397891828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = 1.397891828 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = 1.397891828 + -0.28125 x = 1.397891828 + -0.28125 Combine like terms: 1.397891828 + -0.28125 = 1.116641828 x = 1.116641828 Simplifying x = 1.116641828Subproblem 2
x + 0.28125 = -1.397891828 Simplifying x + 0.28125 = -1.397891828 Reorder the terms: 0.28125 + x = -1.397891828 Solving 0.28125 + x = -1.397891828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = -1.397891828 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = -1.397891828 + -0.28125 x = -1.397891828 + -0.28125 Combine like terms: -1.397891828 + -0.28125 = -1.679141828 x = -1.679141828 Simplifying x = -1.679141828Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.116641828, -1.679141828}
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