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Simplifying 3x2 + 60x + -224 = 0 Reorder the terms: -224 + 60x + 3x2 = 0 Solving -224 + 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'. -74.66666667 + 20x + x2 = 0 Move the constant term to the right: Add '74.66666667' to each side of the equation. -74.66666667 + 20x + 74.66666667 + x2 = 0 + 74.66666667 Reorder the terms: -74.66666667 + 74.66666667 + 20x + x2 = 0 + 74.66666667 Combine like terms: -74.66666667 + 74.66666667 = 0.00000000 0.00000000 + 20x + x2 = 0 + 74.66666667 20x + x2 = 0 + 74.66666667 Combine like terms: 0 + 74.66666667 = 74.66666667 20x + x2 = 74.66666667 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 = 74.66666667 + 100 Reorder the terms: 100 + 20x + x2 = 74.66666667 + 100 Combine like terms: 74.66666667 + 100 = 174.66666667 100 + 20x + x2 = 174.66666667 Factor a perfect square on the left side: (x + 10)(x + 10) = 174.66666667 Calculate the square root of the right side: 13.216151735 Break this problem into two subproblems by setting (x + 10) equal to 13.216151735 and -13.216151735.Subproblem 1
x + 10 = 13.216151735 Simplifying x + 10 = 13.216151735 Reorder the terms: 10 + x = 13.216151735 Solving 10 + x = 13.216151735 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 = 13.216151735 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.216151735 + -10 x = 13.216151735 + -10 Combine like terms: 13.216151735 + -10 = 3.216151735 x = 3.216151735 Simplifying x = 3.216151735Subproblem 2
x + 10 = -13.216151735 Simplifying x + 10 = -13.216151735 Reorder the terms: 10 + x = -13.216151735 Solving 10 + x = -13.216151735 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 = -13.216151735 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.216151735 + -10 x = -13.216151735 + -10 Combine like terms: -13.216151735 + -10 = -23.216151735 x = -23.216151735 Simplifying x = -23.216151735Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.216151735, -23.216151735}
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