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Simplifying 3.5x2 + -400x + -1400 = 0 Reorder the terms: -1400 + -400x + 3.5x2 = 0 Solving -1400 + -400x + 3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -400 + -114.2857143x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -114.2857143x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -114.2857143x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -114.2857143x + x2 = 0 + 400 -114.2857143x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -114.2857143x + x2 = 400 The x term is -114.2857143x. Take half its coefficient (-57.14285715). Square it (3265.306123) and add it to both sides. Add '3265.306123' to each side of the equation. -114.2857143x + 3265.306123 + x2 = 400 + 3265.306123 Reorder the terms: 3265.306123 + -114.2857143x + x2 = 400 + 3265.306123 Combine like terms: 400 + 3265.306123 = 3665.306123 3265.306123 + -114.2857143x + x2 = 3665.306123 Factor a perfect square on the left side: (x + -57.14285715)(x + -57.14285715) = 3665.306123 Calculate the square root of the right side: 60.54177172 Break this problem into two subproblems by setting (x + -57.14285715) equal to 60.54177172 and -60.54177172.Subproblem 1
x + -57.14285715 = 60.54177172 Simplifying x + -57.14285715 = 60.54177172 Reorder the terms: -57.14285715 + x = 60.54177172 Solving -57.14285715 + x = 60.54177172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '57.14285715' to each side of the equation. -57.14285715 + 57.14285715 + x = 60.54177172 + 57.14285715 Combine like terms: -57.14285715 + 57.14285715 = 0.00000000 0.00000000 + x = 60.54177172 + 57.14285715 x = 60.54177172 + 57.14285715 Combine like terms: 60.54177172 + 57.14285715 = 117.68462887 x = 117.68462887 Simplifying x = 117.68462887Subproblem 2
x + -57.14285715 = -60.54177172 Simplifying x + -57.14285715 = -60.54177172 Reorder the terms: -57.14285715 + x = -60.54177172 Solving -57.14285715 + x = -60.54177172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '57.14285715' to each side of the equation. -57.14285715 + 57.14285715 + x = -60.54177172 + 57.14285715 Combine like terms: -57.14285715 + 57.14285715 = 0.00000000 0.00000000 + x = -60.54177172 + 57.14285715 x = -60.54177172 + 57.14285715 Combine like terms: -60.54177172 + 57.14285715 = -3.39891457 x = -3.39891457 Simplifying x = -3.39891457Solution
The solution to the problem is based on the solutions from the subproblems. x = {117.68462887, -3.39891457}
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