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Simplifying 0 = 3x2 + -60x + 1 Reorder the terms: 0 = 1 + -60x + 3x2 Solving 0 = 1 + -60x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 60x + -3x2 = 1 + -60x + 3x2 + -1 + 60x + -3x2 Reorder the terms: -1 + 60x + -3x2 = 1 + -1 + -60x + 60x + 3x2 + -3x2 Combine like terms: 1 + -1 = 0 -1 + 60x + -3x2 = 0 + -60x + 60x + 3x2 + -3x2 -1 + 60x + -3x2 = -60x + 60x + 3x2 + -3x2 Combine like terms: -60x + 60x = 0 -1 + 60x + -3x2 = 0 + 3x2 + -3x2 -1 + 60x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -1 + 60x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.3333333333 + -20x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -20x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -20x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -20x + x2 = 0 + -0.3333333333 -20x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -20x + x2 = -0.3333333333 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 = -0.3333333333 + 100 Reorder the terms: 100 + -20x + x2 = -0.3333333333 + 100 Combine like terms: -0.3333333333 + 100 = 99.6666666667 100 + -20x + x2 = 99.6666666667 Factor a perfect square on the left side: (x + -10)(x + -10) = 99.6666666667 Calculate the square root of the right side: 9.983319421 Break this problem into two subproblems by setting (x + -10) equal to 9.983319421 and -9.983319421.Subproblem 1
x + -10 = 9.983319421 Simplifying x + -10 = 9.983319421 Reorder the terms: -10 + x = 9.983319421 Solving -10 + x = 9.983319421 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 = 9.983319421 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.983319421 + 10 x = 9.983319421 + 10 Combine like terms: 9.983319421 + 10 = 19.983319421 x = 19.983319421 Simplifying x = 19.983319421Subproblem 2
x + -10 = -9.983319421 Simplifying x + -10 = -9.983319421 Reorder the terms: -10 + x = -9.983319421 Solving -10 + x = -9.983319421 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 = -9.983319421 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.983319421 + 10 x = -9.983319421 + 10 Combine like terms: -9.983319421 + 10 = 0.016680579 x = 0.016680579 Simplifying x = 0.016680579Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.983319421, 0.016680579}
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