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Simplifying 2x + -1[3 + -5x(x + -3)] = (2x + -1) + 10 Reorder the terms: 2x + -1[3 + -5x(-3 + x)] = (2x + -1) + 10 2x + -1[3 + (-3 * -5x + x * -5x)] = (2x + -1) + 10 2x + -1[3 + (15x + -5x2)] = (2x + -1) + 10 2x + [3 * -1 + 15x * -1 + -5x2 * -1] = (2x + -1) + 10 2x + [-3 + -15x + 5x2] = (2x + -1) + 10 Reorder the terms: -3 + 2x + -15x + 5x2 = (2x + -1) + 10 Combine like terms: 2x + -15x = -13x -3 + -13x + 5x2 = (2x + -1) + 10 Reorder the terms: -3 + -13x + 5x2 = (-1 + 2x) + 10 Remove parenthesis around (-1 + 2x) -3 + -13x + 5x2 = -1 + 2x + 10 Reorder the terms: -3 + -13x + 5x2 = -1 + 10 + 2x Combine like terms: -1 + 10 = 9 -3 + -13x + 5x2 = 9 + 2x Solving -3 + -13x + 5x2 = 9 + 2x Solving for variable 'x'. Reorder the terms: -3 + -9 + -13x + -2x + 5x2 = 9 + 2x + -9 + -2x Combine like terms: -3 + -9 = -12 -12 + -13x + -2x + 5x2 = 9 + 2x + -9 + -2x Combine like terms: -13x + -2x = -15x -12 + -15x + 5x2 = 9 + 2x + -9 + -2x Reorder the terms: -12 + -15x + 5x2 = 9 + -9 + 2x + -2x Combine like terms: 9 + -9 = 0 -12 + -15x + 5x2 = 0 + 2x + -2x -12 + -15x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -12 + -15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -3x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -3x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -3x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -3x + x2 = 0 + 2.4 -3x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -3x + x2 = 2.4 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 2.4 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2.4 + 2.25 Combine like terms: 2.4 + 2.25 = 4.65 2.25 + -3x + x2 = 4.65 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4.65 Calculate the square root of the right side: 2.156385865 Break this problem into two subproblems by setting (x + -1.5) equal to 2.156385865 and -2.156385865.Subproblem 1
x + -1.5 = 2.156385865 Simplifying x + -1.5 = 2.156385865 Reorder the terms: -1.5 + x = 2.156385865 Solving -1.5 + x = 2.156385865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.156385865 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.156385865 + 1.5 x = 2.156385865 + 1.5 Combine like terms: 2.156385865 + 1.5 = 3.656385865 x = 3.656385865 Simplifying x = 3.656385865Subproblem 2
x + -1.5 = -2.156385865 Simplifying x + -1.5 = -2.156385865 Reorder the terms: -1.5 + x = -2.156385865 Solving -1.5 + x = -2.156385865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.156385865 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.156385865 + 1.5 x = -2.156385865 + 1.5 Combine like terms: -2.156385865 + 1.5 = -0.656385865 x = -0.656385865 Simplifying x = -0.656385865Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.656385865, -0.656385865}
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