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Simplifying 3x + 4x(3 + -5x) = 2 3x + (3 * 4x + -5x * 4x) = 2 3x + (12x + -20x2) = 2 Combine like terms: 3x + 12x = 15x 15x + -20x2 = 2 Solving 15x + -20x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 15x + -20x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 15x + -20x2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. 0.1 + -0.75x + x2 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + -0.75x + -0.1 + x2 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + -0.75x + x2 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + -0.75x + x2 = 0.0 + -0.1 -0.75x + x2 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 -0.75x + x2 = -0.1 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -0.1 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.1 + 0.140625 Combine like terms: -0.1 + 0.140625 = 0.040625 0.140625 + -0.75x + x2 = 0.040625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.040625 Calculate the square root of the right side: 0.201556444 Break this problem into two subproblems by setting (x + -0.375) equal to 0.201556444 and -0.201556444.Subproblem 1
x + -0.375 = 0.201556444 Simplifying x + -0.375 = 0.201556444 Reorder the terms: -0.375 + x = 0.201556444 Solving -0.375 + x = 0.201556444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.201556444 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.201556444 + 0.375 x = 0.201556444 + 0.375 Combine like terms: 0.201556444 + 0.375 = 0.576556444 x = 0.576556444 Simplifying x = 0.576556444Subproblem 2
x + -0.375 = -0.201556444 Simplifying x + -0.375 = -0.201556444 Reorder the terms: -0.375 + x = -0.201556444 Solving -0.375 + x = -0.201556444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.201556444 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.201556444 + 0.375 x = -0.201556444 + 0.375 Combine like terms: -0.201556444 + 0.375 = 0.173443556 x = 0.173443556 Simplifying x = 0.173443556Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.576556444, 0.173443556}
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