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Simplifying (5x + 6)(x + -1) + -2x2 + -5x + 3 = 0 Reorder the terms: (6 + 5x)(x + -1) + -2x2 + -5x + 3 = 0 Reorder the terms: (6 + 5x)(-1 + x) + -2x2 + -5x + 3 = 0 Multiply (6 + 5x) * (-1 + x) (6(-1 + x) + 5x * (-1 + x)) + -2x2 + -5x + 3 = 0 ((-1 * 6 + x * 6) + 5x * (-1 + x)) + -2x2 + -5x + 3 = 0 ((-6 + 6x) + 5x * (-1 + x)) + -2x2 + -5x + 3 = 0 (-6 + 6x + (-1 * 5x + x * 5x)) + -2x2 + -5x + 3 = 0 (-6 + 6x + (-5x + 5x2)) + -2x2 + -5x + 3 = 0 Combine like terms: 6x + -5x = 1x (-6 + 1x + 5x2) + -2x2 + -5x + 3 = 0 Reorder the terms: -6 + 3 + 1x + -5x + 5x2 + -2x2 = 0 Combine like terms: -6 + 3 = -3 -3 + 1x + -5x + 5x2 + -2x2 = 0 Combine like terms: 1x + -5x = -4x -3 + -4x + 5x2 + -2x2 = 0 Combine like terms: 5x2 + -2x2 = 3x2 -3 + -4x + 3x2 = 0 Solving -3 + -4x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.333333333x + x2 = 0 + 1 -1.333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.333333333x + x2 = 1 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 1 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 1 + 0.4444444442 Combine like terms: 1 + 0.4444444442 = 1.4444444442 0.4444444442 + -1.333333333x + x2 = 1.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.201850425 and -1.201850425.Subproblem 1
x + -0.6666666665 = 1.201850425 Simplifying x + -0.6666666665 = 1.201850425 Reorder the terms: -0.6666666665 + x = 1.201850425 Solving -0.6666666665 + x = 1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.201850425 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.201850425 + 0.6666666665 x = 1.201850425 + 0.6666666665 Combine like terms: 1.201850425 + 0.6666666665 = 1.8685170915 x = 1.8685170915 Simplifying x = 1.8685170915Subproblem 2
x + -0.6666666665 = -1.201850425 Simplifying x + -0.6666666665 = -1.201850425 Reorder the terms: -0.6666666665 + x = -1.201850425 Solving -0.6666666665 + x = -1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.201850425 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.201850425 + 0.6666666665 x = -1.201850425 + 0.6666666665 Combine like terms: -1.201850425 + 0.6666666665 = -0.5351837585 x = -0.5351837585 Simplifying x = -0.5351837585Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8685170915, -0.5351837585}
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