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Simplifying (-7x + -6)(x + -5) + (8x + -9) = 0 Reorder the terms: (-6 + -7x)(x + -5) + (8x + -9) = 0 Reorder the terms: (-6 + -7x)(-5 + x) + (8x + -9) = 0 Multiply (-6 + -7x) * (-5 + x) (-6(-5 + x) + -7x * (-5 + x)) + (8x + -9) = 0 ((-5 * -6 + x * -6) + -7x * (-5 + x)) + (8x + -9) = 0 ((30 + -6x) + -7x * (-5 + x)) + (8x + -9) = 0 (30 + -6x + (-5 * -7x + x * -7x)) + (8x + -9) = 0 (30 + -6x + (35x + -7x2)) + (8x + -9) = 0 Combine like terms: -6x + 35x = 29x (30 + 29x + -7x2) + (8x + -9) = 0 Reorder the terms: 30 + 29x + -7x2 + (-9 + 8x) = 0 Remove parenthesis around (-9 + 8x) 30 + 29x + -7x2 + -9 + 8x = 0 Reorder the terms: 30 + -9 + 29x + 8x + -7x2 = 0 Combine like terms: 30 + -9 = 21 21 + 29x + 8x + -7x2 = 0 Combine like terms: 29x + 8x = 37x 21 + 37x + -7x2 = 0 Solving 21 + 37x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -3 + -5.285714286x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -5.285714286x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -5.285714286x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5.285714286x + x2 = 0 + 3 -5.285714286x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5.285714286x + x2 = 3 The x term is -5.285714286x. Take half its coefficient (-2.642857143). Square it (6.984693878) and add it to both sides. Add '6.984693878' to each side of the equation. -5.285714286x + 6.984693878 + x2 = 3 + 6.984693878 Reorder the terms: 6.984693878 + -5.285714286x + x2 = 3 + 6.984693878 Combine like terms: 3 + 6.984693878 = 9.984693878 6.984693878 + -5.285714286x + x2 = 9.984693878 Factor a perfect square on the left side: (x + -2.642857143)(x + -2.642857143) = 9.984693878 Calculate the square root of the right side: 3.159856623 Break this problem into two subproblems by setting (x + -2.642857143) equal to 3.159856623 and -3.159856623.Subproblem 1
x + -2.642857143 = 3.159856623 Simplifying x + -2.642857143 = 3.159856623 Reorder the terms: -2.642857143 + x = 3.159856623 Solving -2.642857143 + x = 3.159856623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.642857143' to each side of the equation. -2.642857143 + 2.642857143 + x = 3.159856623 + 2.642857143 Combine like terms: -2.642857143 + 2.642857143 = 0.000000000 0.000000000 + x = 3.159856623 + 2.642857143 x = 3.159856623 + 2.642857143 Combine like terms: 3.159856623 + 2.642857143 = 5.802713766 x = 5.802713766 Simplifying x = 5.802713766Subproblem 2
x + -2.642857143 = -3.159856623 Simplifying x + -2.642857143 = -3.159856623 Reorder the terms: -2.642857143 + x = -3.159856623 Solving -2.642857143 + x = -3.159856623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.642857143' to each side of the equation. -2.642857143 + 2.642857143 + x = -3.159856623 + 2.642857143 Combine like terms: -2.642857143 + 2.642857143 = 0.000000000 0.000000000 + x = -3.159856623 + 2.642857143 x = -3.159856623 + 2.642857143 Combine like terms: -3.159856623 + 2.642857143 = -0.51699948 x = -0.51699948 Simplifying x = -0.51699948Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.802713766, -0.51699948}
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