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Simplifying 3x2 + 10x + -3600 = 0 Reorder the terms: -3600 + 10x + 3x2 = 0 Solving -3600 + 10x + 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'. -1200 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 3.333333333x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 3.333333333x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 3.333333333x + x2 = 0 + 1200 3.333333333x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 3.333333333x + x2 = 1200 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 1200 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 1200 + 2.777777779 Combine like terms: 1200 + 2.777777779 = 1202.777777779 2.777777779 + 3.333333333x + x2 = 1202.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 1202.777777779 Calculate the square root of the right side: 34.681086744 Break this problem into two subproblems by setting (x + 1.666666667) equal to 34.681086744 and -34.681086744.Subproblem 1
x + 1.666666667 = 34.681086744 Simplifying x + 1.666666667 = 34.681086744 Reorder the terms: 1.666666667 + x = 34.681086744 Solving 1.666666667 + x = 34.681086744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 34.681086744 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 34.681086744 + -1.666666667 x = 34.681086744 + -1.666666667 Combine like terms: 34.681086744 + -1.666666667 = 33.014420077 x = 33.014420077 Simplifying x = 33.014420077Subproblem 2
x + 1.666666667 = -34.681086744 Simplifying x + 1.666666667 = -34.681086744 Reorder the terms: 1.666666667 + x = -34.681086744 Solving 1.666666667 + x = -34.681086744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -34.681086744 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -34.681086744 + -1.666666667 x = -34.681086744 + -1.666666667 Combine like terms: -34.681086744 + -1.666666667 = -36.347753411 x = -36.347753411 Simplifying x = -36.347753411Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.014420077, -36.347753411}
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