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Simplifying 3x2 + 43x + 126 = 0 Reorder the terms: 126 + 43x + 3x2 = 0 Solving 126 + 43x + 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'. 42 + 14.33333333x + x2 = 0 Move the constant term to the right: Add '-42' to each side of the equation. 42 + 14.33333333x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + 14.33333333x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 14.33333333x + x2 = 0 + -42 14.33333333x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 14.33333333x + x2 = -42 The x term is 14.33333333x. Take half its coefficient (7.166666665). Square it (51.36111109) and add it to both sides. Add '51.36111109' to each side of the equation. 14.33333333x + 51.36111109 + x2 = -42 + 51.36111109 Reorder the terms: 51.36111109 + 14.33333333x + x2 = -42 + 51.36111109 Combine like terms: -42 + 51.36111109 = 9.36111109 51.36111109 + 14.33333333x + x2 = 9.36111109 Factor a perfect square on the left side: (x + 7.166666665)(x + 7.166666665) = 9.36111109 Calculate the square root of the right side: 3.059593288 Break this problem into two subproblems by setting (x + 7.166666665) equal to 3.059593288 and -3.059593288.Subproblem 1
x + 7.166666665 = 3.059593288 Simplifying x + 7.166666665 = 3.059593288 Reorder the terms: 7.166666665 + x = 3.059593288 Solving 7.166666665 + x = 3.059593288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.166666665' to each side of the equation. 7.166666665 + -7.166666665 + x = 3.059593288 + -7.166666665 Combine like terms: 7.166666665 + -7.166666665 = 0.000000000 0.000000000 + x = 3.059593288 + -7.166666665 x = 3.059593288 + -7.166666665 Combine like terms: 3.059593288 + -7.166666665 = -4.107073377 x = -4.107073377 Simplifying x = -4.107073377Subproblem 2
x + 7.166666665 = -3.059593288 Simplifying x + 7.166666665 = -3.059593288 Reorder the terms: 7.166666665 + x = -3.059593288 Solving 7.166666665 + x = -3.059593288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.166666665' to each side of the equation. 7.166666665 + -7.166666665 + x = -3.059593288 + -7.166666665 Combine like terms: 7.166666665 + -7.166666665 = 0.000000000 0.000000000 + x = -3.059593288 + -7.166666665 x = -3.059593288 + -7.166666665 Combine like terms: -3.059593288 + -7.166666665 = -10.226259953 x = -10.226259953 Simplifying x = -10.226259953Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.107073377, -10.226259953}
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