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Simplifying 3x2 + -30x + 67 = 0 Reorder the terms: 67 + -30x + 3x2 = 0 Solving 67 + -30x + 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'. 22.33333333 + -10x + x2 = 0 Move the constant term to the right: Add '-22.33333333' to each side of the equation. 22.33333333 + -10x + -22.33333333 + x2 = 0 + -22.33333333 Reorder the terms: 22.33333333 + -22.33333333 + -10x + x2 = 0 + -22.33333333 Combine like terms: 22.33333333 + -22.33333333 = 0.00000000 0.00000000 + -10x + x2 = 0 + -22.33333333 -10x + x2 = 0 + -22.33333333 Combine like terms: 0 + -22.33333333 = -22.33333333 -10x + x2 = -22.33333333 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -22.33333333 + 25 Reorder the terms: 25 + -10x + x2 = -22.33333333 + 25 Combine like terms: -22.33333333 + 25 = 2.66666667 25 + -10x + x2 = 2.66666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 2.66666667 Calculate the square root of the right side: 1.632993163 Break this problem into two subproblems by setting (x + -5) equal to 1.632993163 and -1.632993163.Subproblem 1
x + -5 = 1.632993163 Simplifying x + -5 = 1.632993163 Reorder the terms: -5 + x = 1.632993163 Solving -5 + x = 1.632993163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 1.632993163 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1.632993163 + 5 x = 1.632993163 + 5 Combine like terms: 1.632993163 + 5 = 6.632993163 x = 6.632993163 Simplifying x = 6.632993163Subproblem 2
x + -5 = -1.632993163 Simplifying x + -5 = -1.632993163 Reorder the terms: -5 + x = -1.632993163 Solving -5 + x = -1.632993163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -1.632993163 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1.632993163 + 5 x = -1.632993163 + 5 Combine like terms: -1.632993163 + 5 = 3.367006837 x = 3.367006837 Simplifying x = 3.367006837Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.632993163, 3.367006837}
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