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Simplifying 3x2 + 40x + 45 = 0 Reorder the terms: 45 + 40x + 3x2 = 0 Solving 45 + 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'. 15 + 13.33333333x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + 13.33333333x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 13.33333333x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 13.33333333x + x2 = 0 + -15 13.33333333x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 13.33333333x + x2 = -15 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 = -15 + 44.44444442 Reorder the terms: 44.44444442 + 13.33333333x + x2 = -15 + 44.44444442 Combine like terms: -15 + 44.44444442 = 29.44444442 44.44444442 + 13.33333333x + x2 = 29.44444442 Factor a perfect square on the left side: (x + 6.666666665)(x + 6.666666665) = 29.44444442 Calculate the square root of the right side: 5.42627353 Break this problem into two subproblems by setting (x + 6.666666665) equal to 5.42627353 and -5.42627353.Subproblem 1
x + 6.666666665 = 5.42627353 Simplifying x + 6.666666665 = 5.42627353 Reorder the terms: 6.666666665 + x = 5.42627353 Solving 6.666666665 + x = 5.42627353 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 = 5.42627353 + -6.666666665 Combine like terms: 6.666666665 + -6.666666665 = 0.000000000 0.000000000 + x = 5.42627353 + -6.666666665 x = 5.42627353 + -6.666666665 Combine like terms: 5.42627353 + -6.666666665 = -1.240393135 x = -1.240393135 Simplifying x = -1.240393135Subproblem 2
x + 6.666666665 = -5.42627353 Simplifying x + 6.666666665 = -5.42627353 Reorder the terms: 6.666666665 + x = -5.42627353 Solving 6.666666665 + x = -5.42627353 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 = -5.42627353 + -6.666666665 Combine like terms: 6.666666665 + -6.666666665 = 0.000000000 0.000000000 + x = -5.42627353 + -6.666666665 x = -5.42627353 + -6.666666665 Combine like terms: -5.42627353 + -6.666666665 = -12.092940195 x = -12.092940195 Simplifying x = -12.092940195Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.240393135, -12.092940195}
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