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Simplifying (2x + 1)(-3x + 2) = -5x + 2 + -1 Reorder the terms: (1 + 2x)(-3x + 2) = -5x + 2 + -1 Reorder the terms: (1 + 2x)(2 + -3x) = -5x + 2 + -1 Multiply (1 + 2x) * (2 + -3x) (1(2 + -3x) + 2x * (2 + -3x)) = -5x + 2 + -1 ((2 * 1 + -3x * 1) + 2x * (2 + -3x)) = -5x + 2 + -1 ((2 + -3x) + 2x * (2 + -3x)) = -5x + 2 + -1 (2 + -3x + (2 * 2x + -3x * 2x)) = -5x + 2 + -1 (2 + -3x + (4x + -6x2)) = -5x + 2 + -1 Combine like terms: -3x + 4x = 1x (2 + 1x + -6x2) = -5x + 2 + -1 Reorder the terms: 2 + 1x + -6x2 = 2 + -1 + -5x Combine like terms: 2 + -1 = 1 2 + 1x + -6x2 = 1 + -5x Solving 2 + 1x + -6x2 = 1 + -5x Solving for variable 'x'. Reorder the terms: 2 + -1 + 1x + 5x + -6x2 = 1 + -5x + -1 + 5x Combine like terms: 2 + -1 = 1 1 + 1x + 5x + -6x2 = 1 + -5x + -1 + 5x Combine like terms: 1x + 5x = 6x 1 + 6x + -6x2 = 1 + -5x + -1 + 5x Reorder the terms: 1 + 6x + -6x2 = 1 + -1 + -5x + 5x Combine like terms: 1 + -1 = 0 1 + 6x + -6x2 = 0 + -5x + 5x 1 + 6x + -6x2 = -5x + 5x Combine like terms: -5x + 5x = 0 1 + 6x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.1666666667 + -1x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -1x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -1x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.1666666667 -1x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -1x + x2 = 0.1666666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.1666666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.1666666667 + 0.25 Combine like terms: 0.1666666667 + 0.25 = 0.4166666667 0.25 + -1x + x2 = 0.4166666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.4166666667 Calculate the square root of the right side: 0.645497224 Break this problem into two subproblems by setting (x + -0.5) equal to 0.645497224 and -0.645497224.Subproblem 1
x + -0.5 = 0.645497224 Simplifying x + -0.5 = 0.645497224 Reorder the terms: -0.5 + x = 0.645497224 Solving -0.5 + x = 0.645497224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.645497224 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.645497224 + 0.5 x = 0.645497224 + 0.5 Combine like terms: 0.645497224 + 0.5 = 1.145497224 x = 1.145497224 Simplifying x = 1.145497224Subproblem 2
x + -0.5 = -0.645497224 Simplifying x + -0.5 = -0.645497224 Reorder the terms: -0.5 + x = -0.645497224 Solving -0.5 + x = -0.645497224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.645497224 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.645497224 + 0.5 x = -0.645497224 + 0.5 Combine like terms: -0.645497224 + 0.5 = -0.145497224 x = -0.145497224 Simplifying x = -0.145497224Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.145497224, -0.145497224}
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