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Simplifying (5x + -0.4)(7x + 0.8) = 0 Reorder the terms: (-0.4 + 5x)(7x + 0.8) = 0 Reorder the terms: (-0.4 + 5x)(0.8 + 7x) = 0 Multiply (-0.4 + 5x) * (0.8 + 7x) (-0.4(0.8 + 7x) + 5x * (0.8 + 7x)) = 0 ((0.8 * -0.4 + 7x * -0.4) + 5x * (0.8 + 7x)) = 0 ((-0.32 + -2.8x) + 5x * (0.8 + 7x)) = 0 (-0.32 + -2.8x + (0.8 * 5x + 7x * 5x)) = 0 (-0.32 + -2.8x + (4x + 35x2)) = 0 Combine like terms: -2.8x + 4x = 1.2x (-0.32 + 1.2x + 35x2) = 0 Solving -0.32 + 1.2x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.009142857143 + 0.03428571429x + x2 = 0 Move the constant term to the right: Add '0.009142857143' to each side of the equation. -0.009142857143 + 0.03428571429x + 0.009142857143 + x2 = 0 + 0.009142857143 Reorder the terms: -0.009142857143 + 0.009142857143 + 0.03428571429x + x2 = 0 + 0.009142857143 Combine like terms: -0.009142857143 + 0.009142857143 = 0.000000000000 0.000000000000 + 0.03428571429x + x2 = 0 + 0.009142857143 0.03428571429x + x2 = 0 + 0.009142857143 Combine like terms: 0 + 0.009142857143 = 0.009142857143 0.03428571429x + x2 = 0.009142857143 The x term is 0.03428571429x. Take half its coefficient (0.01714285715). Square it (0.0002938775513) and add it to both sides. Add '0.0002938775513' to each side of the equation. 0.03428571429x + 0.0002938775513 + x2 = 0.009142857143 + 0.0002938775513 Reorder the terms: 0.0002938775513 + 0.03428571429x + x2 = 0.009142857143 + 0.0002938775513 Combine like terms: 0.009142857143 + 0.0002938775513 = 0.0094367346943 0.0002938775513 + 0.03428571429x + x2 = 0.0094367346943 Factor a perfect square on the left side: (x + 0.01714285715)(x + 0.01714285715) = 0.0094367346943 Calculate the square root of the right side: 0.097142857 Break this problem into two subproblems by setting (x + 0.01714285715) equal to 0.097142857 and -0.097142857.Subproblem 1
x + 0.01714285715 = 0.097142857 Simplifying x + 0.01714285715 = 0.097142857 Reorder the terms: 0.01714285715 + x = 0.097142857 Solving 0.01714285715 + x = 0.097142857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01714285715' to each side of the equation. 0.01714285715 + -0.01714285715 + x = 0.097142857 + -0.01714285715 Combine like terms: 0.01714285715 + -0.01714285715 = 0.00000000000 0.00000000000 + x = 0.097142857 + -0.01714285715 x = 0.097142857 + -0.01714285715 Combine like terms: 0.097142857 + -0.01714285715 = 0.07999999985 x = 0.07999999985 Simplifying x = 0.07999999985Subproblem 2
x + 0.01714285715 = -0.097142857 Simplifying x + 0.01714285715 = -0.097142857 Reorder the terms: 0.01714285715 + x = -0.097142857 Solving 0.01714285715 + x = -0.097142857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01714285715' to each side of the equation. 0.01714285715 + -0.01714285715 + x = -0.097142857 + -0.01714285715 Combine like terms: 0.01714285715 + -0.01714285715 = 0.00000000000 0.00000000000 + x = -0.097142857 + -0.01714285715 x = -0.097142857 + -0.01714285715 Combine like terms: -0.097142857 + -0.01714285715 = -0.11428571415 x = -0.11428571415 Simplifying x = -0.11428571415Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.07999999985, -0.11428571415}
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