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Simplifying 7x(2x + -1) = 8x + 5 Reorder the terms: 7x(-1 + 2x) = 8x + 5 (-1 * 7x + 2x * 7x) = 8x + 5 (-7x + 14x2) = 8x + 5 Reorder the terms: -7x + 14x2 = 5 + 8x Solving -7x + 14x2 = 5 + 8x Solving for variable 'x'. Reorder the terms: -5 + -7x + -8x + 14x2 = 5 + 8x + -5 + -8x Combine like terms: -7x + -8x = -15x -5 + -15x + 14x2 = 5 + 8x + -5 + -8x Reorder the terms: -5 + -15x + 14x2 = 5 + -5 + 8x + -8x Combine like terms: 5 + -5 = 0 -5 + -15x + 14x2 = 0 + 8x + -8x -5 + -15x + 14x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -5 + -15x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.3571428571 + -1.071428571x + x2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + -1.071428571x + 0.3571428571 + x2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + -1.071428571x + x2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + -1.071428571x + x2 = 0 + 0.3571428571 -1.071428571x + x2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 -1.071428571x + x2 = 0.3571428571 The x term is -1.071428571x. Take half its coefficient (-0.5357142855). Square it (0.2869897957) and add it to both sides. Add '0.2869897957' to each side of the equation. -1.071428571x + 0.2869897957 + x2 = 0.3571428571 + 0.2869897957 Reorder the terms: 0.2869897957 + -1.071428571x + x2 = 0.3571428571 + 0.2869897957 Combine like terms: 0.3571428571 + 0.2869897957 = 0.6441326528 0.2869897957 + -1.071428571x + x2 = 0.6441326528 Factor a perfect square on the left side: (x + -0.5357142855)(x + -0.5357142855) = 0.6441326528 Calculate the square root of the right side: 0.802578752 Break this problem into two subproblems by setting (x + -0.5357142855) equal to 0.802578752 and -0.802578752.Subproblem 1
x + -0.5357142855 = 0.802578752 Simplifying x + -0.5357142855 = 0.802578752 Reorder the terms: -0.5357142855 + x = 0.802578752 Solving -0.5357142855 + x = 0.802578752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5357142855' to each side of the equation. -0.5357142855 + 0.5357142855 + x = 0.802578752 + 0.5357142855 Combine like terms: -0.5357142855 + 0.5357142855 = 0.0000000000 0.0000000000 + x = 0.802578752 + 0.5357142855 x = 0.802578752 + 0.5357142855 Combine like terms: 0.802578752 + 0.5357142855 = 1.3382930375 x = 1.3382930375 Simplifying x = 1.3382930375Subproblem 2
x + -0.5357142855 = -0.802578752 Simplifying x + -0.5357142855 = -0.802578752 Reorder the terms: -0.5357142855 + x = -0.802578752 Solving -0.5357142855 + x = -0.802578752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5357142855' to each side of the equation. -0.5357142855 + 0.5357142855 + x = -0.802578752 + 0.5357142855 Combine like terms: -0.5357142855 + 0.5357142855 = 0.0000000000 0.0000000000 + x = -0.802578752 + 0.5357142855 x = -0.802578752 + 0.5357142855 Combine like terms: -0.802578752 + 0.5357142855 = -0.2668644665 x = -0.2668644665 Simplifying x = -0.2668644665Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3382930375, -0.2668644665}
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