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Simplifying 3x2 + 60x + 100 = 0 Reorder the terms: 100 + 60x + 3x2 = 0 Solving 100 + 60x + 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'. 33.33333333 + 20x + x2 = 0 Move the constant term to the right: Add '-33.33333333' to each side of the equation. 33.33333333 + 20x + -33.33333333 + x2 = 0 + -33.33333333 Reorder the terms: 33.33333333 + -33.33333333 + 20x + x2 = 0 + -33.33333333 Combine like terms: 33.33333333 + -33.33333333 = 0.00000000 0.00000000 + 20x + x2 = 0 + -33.33333333 20x + x2 = 0 + -33.33333333 Combine like terms: 0 + -33.33333333 = -33.33333333 20x + x2 = -33.33333333 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -33.33333333 + 100 Reorder the terms: 100 + 20x + x2 = -33.33333333 + 100 Combine like terms: -33.33333333 + 100 = 66.66666667 100 + 20x + x2 = 66.66666667 Factor a perfect square on the left side: (x + 10)(x + 10) = 66.66666667 Calculate the square root of the right side: 8.164965809 Break this problem into two subproblems by setting (x + 10) equal to 8.164965809 and -8.164965809.Subproblem 1
x + 10 = 8.164965809 Simplifying x + 10 = 8.164965809 Reorder the terms: 10 + x = 8.164965809 Solving 10 + x = 8.164965809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 8.164965809 + -10 Combine like terms: 10 + -10 = 0 0 + x = 8.164965809 + -10 x = 8.164965809 + -10 Combine like terms: 8.164965809 + -10 = -1.835034191 x = -1.835034191 Simplifying x = -1.835034191Subproblem 2
x + 10 = -8.164965809 Simplifying x + 10 = -8.164965809 Reorder the terms: 10 + x = -8.164965809 Solving 10 + x = -8.164965809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -8.164965809 + -10 Combine like terms: 10 + -10 = 0 0 + x = -8.164965809 + -10 x = -8.164965809 + -10 Combine like terms: -8.164965809 + -10 = -18.164965809 x = -18.164965809 Simplifying x = -18.164965809Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.835034191, -18.164965809}
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