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Simplifying 3x2 + -30x + 61 = 0 Reorder the terms: 61 + -30x + 3x2 = 0 Solving 61 + -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'. 20.33333333 + -10x + x2 = 0 Move the constant term to the right: Add '-20.33333333' to each side of the equation. 20.33333333 + -10x + -20.33333333 + x2 = 0 + -20.33333333 Reorder the terms: 20.33333333 + -20.33333333 + -10x + x2 = 0 + -20.33333333 Combine like terms: 20.33333333 + -20.33333333 = 0.00000000 0.00000000 + -10x + x2 = 0 + -20.33333333 -10x + x2 = 0 + -20.33333333 Combine like terms: 0 + -20.33333333 = -20.33333333 -10x + x2 = -20.33333333 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 = -20.33333333 + 25 Reorder the terms: 25 + -10x + x2 = -20.33333333 + 25 Combine like terms: -20.33333333 + 25 = 4.66666667 25 + -10x + x2 = 4.66666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 4.66666667 Calculate the square root of the right side: 2.1602469 Break this problem into two subproblems by setting (x + -5) equal to 2.1602469 and -2.1602469.Subproblem 1
x + -5 = 2.1602469 Simplifying x + -5 = 2.1602469 Reorder the terms: -5 + x = 2.1602469 Solving -5 + x = 2.1602469 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 = 2.1602469 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.1602469 + 5 x = 2.1602469 + 5 Combine like terms: 2.1602469 + 5 = 7.1602469 x = 7.1602469 Simplifying x = 7.1602469Subproblem 2
x + -5 = -2.1602469 Simplifying x + -5 = -2.1602469 Reorder the terms: -5 + x = -2.1602469 Solving -5 + x = -2.1602469 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 = -2.1602469 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.1602469 + 5 x = -2.1602469 + 5 Combine like terms: -2.1602469 + 5 = 2.8397531 x = 2.8397531 Simplifying x = 2.8397531Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.1602469, 2.8397531}
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