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Simplifying 3x2 + -5x + -370 = 0 Reorder the terms: -370 + -5x + 3x2 = 0 Solving -370 + -5x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -123.3333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '123.3333333' to each side of the equation. -123.3333333 + -1.666666667x + 123.3333333 + x2 = 0 + 123.3333333 Reorder the terms: -123.3333333 + 123.3333333 + -1.666666667x + x2 = 0 + 123.3333333 Combine like terms: -123.3333333 + 123.3333333 = 0.0000000 0.0000000 + -1.666666667x + x2 = 0 + 123.3333333 -1.666666667x + x2 = 0 + 123.3333333 Combine like terms: 0 + 123.3333333 = 123.3333333 -1.666666667x + x2 = 123.3333333 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 123.3333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 123.3333333 + 0.6944444447 Combine like terms: 123.3333333 + 0.6944444447 = 124.0277777447 0.6944444447 + -1.666666667x + x2 = 124.0277777447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 124.0277777447 Calculate the square root of the right side: 11.136775913 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 11.136775913 and -11.136775913.Subproblem 1
x + -0.8333333335 = 11.136775913 Simplifying x + -0.8333333335 = 11.136775913 Reorder the terms: -0.8333333335 + x = 11.136775913 Solving -0.8333333335 + x = 11.136775913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 11.136775913 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 11.136775913 + 0.8333333335 x = 11.136775913 + 0.8333333335 Combine like terms: 11.136775913 + 0.8333333335 = 11.9701092465 x = 11.9701092465 Simplifying x = 11.9701092465Subproblem 2
x + -0.8333333335 = -11.136775913 Simplifying x + -0.8333333335 = -11.136775913 Reorder the terms: -0.8333333335 + x = -11.136775913 Solving -0.8333333335 + x = -11.136775913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -11.136775913 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -11.136775913 + 0.8333333335 x = -11.136775913 + 0.8333333335 Combine like terms: -11.136775913 + 0.8333333335 = -10.3034425795 x = -10.3034425795 Simplifying x = -10.3034425795Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.9701092465, -10.3034425795}
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