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Simplifying 3x2 + 40x + 30 = 0 Reorder the terms: 30 + 40x + 3x2 = 0 Solving 30 + 40x + 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'. 10 + 13.33333333x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 13.33333333x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 13.33333333x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 13.33333333x + x2 = 0 + -10 13.33333333x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 13.33333333x + x2 = -10 The x term is 13.33333333x. Take half its coefficient (6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. 13.33333333x + 44.44444442 + x2 = -10 + 44.44444442 Reorder the terms: 44.44444442 + 13.33333333x + x2 = -10 + 44.44444442 Combine like terms: -10 + 44.44444442 = 34.44444442 44.44444442 + 13.33333333x + x2 = 34.44444442 Factor a perfect square on the left side: (x + 6.666666665)(x + 6.666666665) = 34.44444442 Calculate the square root of the right side: 5.868938952 Break this problem into two subproblems by setting (x + 6.666666665) equal to 5.868938952 and -5.868938952.Subproblem 1
x + 6.666666665 = 5.868938952 Simplifying x + 6.666666665 = 5.868938952 Reorder the terms: 6.666666665 + x = 5.868938952 Solving 6.666666665 + x = 5.868938952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.666666665' to each side of the equation. 6.666666665 + -6.666666665 + x = 5.868938952 + -6.666666665 Combine like terms: 6.666666665 + -6.666666665 = 0.000000000 0.000000000 + x = 5.868938952 + -6.666666665 x = 5.868938952 + -6.666666665 Combine like terms: 5.868938952 + -6.666666665 = -0.797727713 x = -0.797727713 Simplifying x = -0.797727713Subproblem 2
x + 6.666666665 = -5.868938952 Simplifying x + 6.666666665 = -5.868938952 Reorder the terms: 6.666666665 + x = -5.868938952 Solving 6.666666665 + x = -5.868938952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.666666665' to each side of the equation. 6.666666665 + -6.666666665 + x = -5.868938952 + -6.666666665 Combine like terms: 6.666666665 + -6.666666665 = 0.000000000 0.000000000 + x = -5.868938952 + -6.666666665 x = -5.868938952 + -6.666666665 Combine like terms: -5.868938952 + -6.666666665 = -12.535605617 x = -12.535605617 Simplifying x = -12.535605617Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.797727713, -12.535605617}
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