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Simplifying 3x2 + 30x + 32 = 0 Reorder the terms: 32 + 30x + 3x2 = 0 Solving 32 + 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'. 10.66666667 + 10x + x2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + 10x + -10.66666667 + x2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + 10x + x2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + 10x + x2 = 0 + -10.66666667 10x + x2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 10x + x2 = -10.66666667 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 = -10.66666667 + 25 Reorder the terms: 25 + 10x + x2 = -10.66666667 + 25 Combine like terms: -10.66666667 + 25 = 14.33333333 25 + 10x + x2 = 14.33333333 Factor a perfect square on the left side: (x + 5)(x + 5) = 14.33333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (x + 5) equal to 3.785938897 and -3.785938897.Subproblem 1
x + 5 = 3.785938897 Simplifying x + 5 = 3.785938897 Reorder the terms: 5 + x = 3.785938897 Solving 5 + x = 3.785938897 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 = 3.785938897 + -5 Combine like terms: 5 + -5 = 0 0 + x = 3.785938897 + -5 x = 3.785938897 + -5 Combine like terms: 3.785938897 + -5 = -1.214061103 x = -1.214061103 Simplifying x = -1.214061103Subproblem 2
x + 5 = -3.785938897 Simplifying x + 5 = -3.785938897 Reorder the terms: 5 + x = -3.785938897 Solving 5 + x = -3.785938897 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 = -3.785938897 + -5 Combine like terms: 5 + -5 = 0 0 + x = -3.785938897 + -5 x = -3.785938897 + -5 Combine like terms: -3.785938897 + -5 = -8.785938897 x = -8.785938897 Simplifying x = -8.785938897Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.214061103, -8.785938897}
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