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Simplifying 4x + -7x(5x + -8) = x + -8 Reorder the terms: 4x + -7x(-8 + 5x) = x + -8 4x + (-8 * -7x + 5x * -7x) = x + -8 4x + (56x + -35x2) = x + -8 Combine like terms: 4x + 56x = 60x 60x + -35x2 = x + -8 Reorder the terms: 60x + -35x2 = -8 + x Solving 60x + -35x2 = -8 + x Solving for variable 'x'. Reorder the terms: 8 + 60x + -1x + -35x2 = -8 + x + 8 + -1x Combine like terms: 60x + -1x = 59x 8 + 59x + -35x2 = -8 + x + 8 + -1x Reorder the terms: 8 + 59x + -35x2 = -8 + 8 + x + -1x Combine like terms: -8 + 8 = 0 8 + 59x + -35x2 = 0 + x + -1x 8 + 59x + -35x2 = x + -1x Combine like terms: x + -1x = 0 8 + 59x + -35x2 = 0 Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -0.2285714286 + -1.685714286x + x2 = 0 Move the constant term to the right: Add '0.2285714286' to each side of the equation. -0.2285714286 + -1.685714286x + 0.2285714286 + x2 = 0 + 0.2285714286 Reorder the terms: -0.2285714286 + 0.2285714286 + -1.685714286x + x2 = 0 + 0.2285714286 Combine like terms: -0.2285714286 + 0.2285714286 = 0.0000000000 0.0000000000 + -1.685714286x + x2 = 0 + 0.2285714286 -1.685714286x + x2 = 0 + 0.2285714286 Combine like terms: 0 + 0.2285714286 = 0.2285714286 -1.685714286x + x2 = 0.2285714286 The x term is -1.685714286x. Take half its coefficient (-0.842857143). Square it (0.7104081635) and add it to both sides. Add '0.7104081635' to each side of the equation. -1.685714286x + 0.7104081635 + x2 = 0.2285714286 + 0.7104081635 Reorder the terms: 0.7104081635 + -1.685714286x + x2 = 0.2285714286 + 0.7104081635 Combine like terms: 0.2285714286 + 0.7104081635 = 0.9389795921 0.7104081635 + -1.685714286x + x2 = 0.9389795921 Factor a perfect square on the left side: (x + -0.842857143)(x + -0.842857143) = 0.9389795921 Calculate the square root of the right side: 0.969009593 Break this problem into two subproblems by setting (x + -0.842857143) equal to 0.969009593 and -0.969009593.Subproblem 1
x + -0.842857143 = 0.969009593 Simplifying x + -0.842857143 = 0.969009593 Reorder the terms: -0.842857143 + x = 0.969009593 Solving -0.842857143 + x = 0.969009593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.842857143' to each side of the equation. -0.842857143 + 0.842857143 + x = 0.969009593 + 0.842857143 Combine like terms: -0.842857143 + 0.842857143 = 0.000000000 0.000000000 + x = 0.969009593 + 0.842857143 x = 0.969009593 + 0.842857143 Combine like terms: 0.969009593 + 0.842857143 = 1.811866736 x = 1.811866736 Simplifying x = 1.811866736Subproblem 2
x + -0.842857143 = -0.969009593 Simplifying x + -0.842857143 = -0.969009593 Reorder the terms: -0.842857143 + x = -0.969009593 Solving -0.842857143 + x = -0.969009593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.842857143' to each side of the equation. -0.842857143 + 0.842857143 + x = -0.969009593 + 0.842857143 Combine like terms: -0.842857143 + 0.842857143 = 0.000000000 0.000000000 + x = -0.969009593 + 0.842857143 x = -0.969009593 + 0.842857143 Combine like terms: -0.969009593 + 0.842857143 = -0.12615245 x = -0.12615245 Simplifying x = -0.12615245Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.811866736, -0.12615245}
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