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Simplifying 3(4x + 1) + 2x(1 + -5x) = 2 + x Reorder the terms: 3(1 + 4x) + 2x(1 + -5x) = 2 + x (1 * 3 + 4x * 3) + 2x(1 + -5x) = 2 + x (3 + 12x) + 2x(1 + -5x) = 2 + x 3 + 12x + (1 * 2x + -5x * 2x) = 2 + x 3 + 12x + (2x + -10x2) = 2 + x Combine like terms: 12x + 2x = 14x 3 + 14x + -10x2 = 2 + x Solving 3 + 14x + -10x2 = 2 + x Solving for variable 'x'. Reorder the terms: 3 + -2 + 14x + -1x + -10x2 = 2 + x + -2 + -1x Combine like terms: 3 + -2 = 1 1 + 14x + -1x + -10x2 = 2 + x + -2 + -1x Combine like terms: 14x + -1x = 13x 1 + 13x + -10x2 = 2 + x + -2 + -1x Reorder the terms: 1 + 13x + -10x2 = 2 + -2 + x + -1x Combine like terms: 2 + -2 = 0 1 + 13x + -10x2 = 0 + x + -1x 1 + 13x + -10x2 = x + -1x Combine like terms: x + -1x = 0 1 + 13x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.1 + -1.3x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -1.3x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + -1.3x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -1.3x + x2 = 0.0 + 0.1 -1.3x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 -1.3x + x2 = 0.1 The x term is -1.3x. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x + 0.4225 + x2 = 0.1 + 0.4225 Reorder the terms: 0.4225 + -1.3x + x2 = 0.1 + 0.4225 Combine like terms: 0.1 + 0.4225 = 0.5225 0.4225 + -1.3x + x2 = 0.5225 Factor a perfect square on the left side: (x + -0.65)(x + -0.65) = 0.5225 Calculate the square root of the right side: 0.722841615 Break this problem into two subproblems by setting (x + -0.65) equal to 0.722841615 and -0.722841615.Subproblem 1
x + -0.65 = 0.722841615 Simplifying x + -0.65 = 0.722841615 Reorder the terms: -0.65 + x = 0.722841615 Solving -0.65 + x = 0.722841615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = 0.722841615 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = 0.722841615 + 0.65 x = 0.722841615 + 0.65 Combine like terms: 0.722841615 + 0.65 = 1.372841615 x = 1.372841615 Simplifying x = 1.372841615Subproblem 2
x + -0.65 = -0.722841615 Simplifying x + -0.65 = -0.722841615 Reorder the terms: -0.65 + x = -0.722841615 Solving -0.65 + x = -0.722841615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = -0.722841615 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = -0.722841615 + 0.65 x = -0.722841615 + 0.65 Combine like terms: -0.722841615 + 0.65 = -0.072841615 x = -0.072841615 Simplifying x = -0.072841615Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.372841615, -0.072841615}
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