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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 = 133.33333333 100 + -20x + x2 = 133.33333333 Factor a perfect square on the left side: (x + -10)(x + -10) = 133.33333333 Calculate the square root of the right side: 11.547005384 Break this problem into two subproblems by setting (x + -10) equal to 11.547005384 and -11.547005384.Subproblem 1
x + -10 = 11.547005384 Simplifying x + -10 = 11.547005384 Reorder the terms: -10 + x = 11.547005384 Solving -10 + x = 11.547005384 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 = 11.547005384 + 10 Combine like terms: -10 + 10 = 0 0 + x = 11.547005384 + 10 x = 11.547005384 + 10 Combine like terms: 11.547005384 + 10 = 21.547005384 x = 21.547005384 Simplifying x = 21.547005384Subproblem 2
x + -10 = -11.547005384 Simplifying x + -10 = -11.547005384 Reorder the terms: -10 + x = -11.547005384 Solving -10 + x = -11.547005384 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 = -11.547005384 + 10 Combine like terms: -10 + 10 = 0 0 + x = -11.547005384 + 10 x = -11.547005384 + 10 Combine like terms: -11.547005384 + 10 = -1.547005384 x = -1.547005384 Simplifying x = -1.547005384Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.547005384, -1.547005384}
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