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Simplifying 3x2 + 60x + -1600 = 0 Reorder the terms: -1600 + 60x + 3x2 = 0 Solving -1600 + 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'. -533.3333333 + 20x + x2 = 0 Move the constant term to the right: Add '533.3333333' to each side of the equation. -533.3333333 + 20x + 533.3333333 + x2 = 0 + 533.3333333 Reorder the terms: -533.3333333 + 533.3333333 + 20x + x2 = 0 + 533.3333333 Combine like terms: -533.3333333 + 533.3333333 = 0.0000000 0.0000000 + 20x + x2 = 0 + 533.3333333 20x + x2 = 0 + 533.3333333 Combine like terms: 0 + 533.3333333 = 533.3333333 20x + x2 = 533.3333333 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 = 533.3333333 + 100 Reorder the terms: 100 + 20x + x2 = 533.3333333 + 100 Combine like terms: 533.3333333 + 100 = 633.3333333 100 + 20x + x2 = 633.3333333 Factor a perfect square on the left side: (x + 10)(x + 10) = 633.3333333 Calculate the square root of the right side: 25.166114784 Break this problem into two subproblems by setting (x + 10) equal to 25.166114784 and -25.166114784.Subproblem 1
x + 10 = 25.166114784 Simplifying x + 10 = 25.166114784 Reorder the terms: 10 + x = 25.166114784 Solving 10 + x = 25.166114784 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 = 25.166114784 + -10 Combine like terms: 10 + -10 = 0 0 + x = 25.166114784 + -10 x = 25.166114784 + -10 Combine like terms: 25.166114784 + -10 = 15.166114784 x = 15.166114784 Simplifying x = 15.166114784Subproblem 2
x + 10 = -25.166114784 Simplifying x + 10 = -25.166114784 Reorder the terms: 10 + x = -25.166114784 Solving 10 + x = -25.166114784 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 = -25.166114784 + -10 Combine like terms: 10 + -10 = 0 0 + x = -25.166114784 + -10 x = -25.166114784 + -10 Combine like terms: -25.166114784 + -10 = -35.166114784 x = -35.166114784 Simplifying x = -35.166114784Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.166114784, -35.166114784}
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