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Simplifying 0 = 30 + -34x + 3x2 Solving 0 = 30 + -34x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + 34x + -3x2 = 30 + -34x + 3x2 + -30 + 34x + -3x2 Reorder the terms: -30 + 34x + -3x2 = 30 + -30 + -34x + 34x + 3x2 + -3x2 Combine like terms: 30 + -30 = 0 -30 + 34x + -3x2 = 0 + -34x + 34x + 3x2 + -3x2 -30 + 34x + -3x2 = -34x + 34x + 3x2 + -3x2 Combine like terms: -34x + 34x = 0 -30 + 34x + -3x2 = 0 + 3x2 + -3x2 -30 + 34x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -30 + 34x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 10 + -11.33333333x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -11.33333333x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -11.33333333x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -11.33333333x + x2 = 0 + -10 -11.33333333x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -11.33333333x + x2 = -10 The x term is -11.33333333x. Take half its coefficient (-5.666666665). Square it (32.11111109) and add it to both sides. Add '32.11111109' to each side of the equation. -11.33333333x + 32.11111109 + x2 = -10 + 32.11111109 Reorder the terms: 32.11111109 + -11.33333333x + x2 = -10 + 32.11111109 Combine like terms: -10 + 32.11111109 = 22.11111109 32.11111109 + -11.33333333x + x2 = 22.11111109 Factor a perfect square on the left side: (x + -5.666666665)(x + -5.666666665) = 22.11111109 Calculate the square root of the right side: 4.702245324 Break this problem into two subproblems by setting (x + -5.666666665) equal to 4.702245324 and -4.702245324.Subproblem 1
x + -5.666666665 = 4.702245324 Simplifying x + -5.666666665 = 4.702245324 Reorder the terms: -5.666666665 + x = 4.702245324 Solving -5.666666665 + x = 4.702245324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = 4.702245324 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = 4.702245324 + 5.666666665 x = 4.702245324 + 5.666666665 Combine like terms: 4.702245324 + 5.666666665 = 10.368911989 x = 10.368911989 Simplifying x = 10.368911989Subproblem 2
x + -5.666666665 = -4.702245324 Simplifying x + -5.666666665 = -4.702245324 Reorder the terms: -5.666666665 + x = -4.702245324 Solving -5.666666665 + x = -4.702245324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = -4.702245324 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = -4.702245324 + 5.666666665 x = -4.702245324 + 5.666666665 Combine like terms: -4.702245324 + 5.666666665 = 0.964421341 x = 0.964421341 Simplifying x = 0.964421341Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.368911989, 0.964421341}
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