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Simplifying 4(1 + -5x) + -5x(7x + -2) = 0 (1 * 4 + -5x * 4) + -5x(7x + -2) = 0 (4 + -20x) + -5x(7x + -2) = 0 Reorder the terms: 4 + -20x + -5x(-2 + 7x) = 0 4 + -20x + (-2 * -5x + 7x * -5x) = 0 4 + -20x + (10x + -35x2) = 0 Combine like terms: -20x + 10x = -10x 4 + -10x + -35x2 = 0 Solving 4 + -10x + -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'. -0.1142857143 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.1142857143' to each side of the equation. -0.1142857143 + 0.2857142857x + 0.1142857143 + x2 = 0 + 0.1142857143 Reorder the terms: -0.1142857143 + 0.1142857143 + 0.2857142857x + x2 = 0 + 0.1142857143 Combine like terms: -0.1142857143 + 0.1142857143 = 0.0000000000 0.0000000000 + 0.2857142857x + x2 = 0 + 0.1142857143 0.2857142857x + x2 = 0 + 0.1142857143 Combine like terms: 0 + 0.1142857143 = 0.1142857143 0.2857142857x + x2 = 0.1142857143 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = 0.1142857143 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 0.1142857143 + 0.02040816328 Combine like terms: 0.1142857143 + 0.02040816328 = 0.13469387758 0.02040816328 + 0.2857142857x + x2 = 0.13469387758 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 0.13469387758 Calculate the square root of the right side: 0.367006645 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 0.367006645 and -0.367006645.Subproblem 1
x + 0.1428571429 = 0.367006645 Simplifying x + 0.1428571429 = 0.367006645 Reorder the terms: 0.1428571429 + x = 0.367006645 Solving 0.1428571429 + x = 0.367006645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 0.367006645 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.367006645 + -0.1428571429 x = 0.367006645 + -0.1428571429 Combine like terms: 0.367006645 + -0.1428571429 = 0.2241495021 x = 0.2241495021 Simplifying x = 0.2241495021Subproblem 2
x + 0.1428571429 = -0.367006645 Simplifying x + 0.1428571429 = -0.367006645 Reorder the terms: 0.1428571429 + x = -0.367006645 Solving 0.1428571429 + x = -0.367006645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -0.367006645 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.367006645 + -0.1428571429 x = -0.367006645 + -0.1428571429 Combine like terms: -0.367006645 + -0.1428571429 = -0.5098637879 x = -0.5098637879 Simplifying x = -0.5098637879Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2241495021, -0.5098637879}
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