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Simplifying 60x + -3x2 + 1 = 0 Reorder the terms: 1 + 60x + -3x2 = 0 Solving 1 + 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'. -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 = 100.3333333333 100 + -20x + x2 = 100.3333333333 Factor a perfect square on the left side: (x + -10)(x + -10) = 100.3333333333 Calculate the square root of the right side: 10.016652801 Break this problem into two subproblems by setting (x + -10) equal to 10.016652801 and -10.016652801.Subproblem 1
x + -10 = 10.016652801 Simplifying x + -10 = 10.016652801 Reorder the terms: -10 + x = 10.016652801 Solving -10 + x = 10.016652801 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 = 10.016652801 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.016652801 + 10 x = 10.016652801 + 10 Combine like terms: 10.016652801 + 10 = 20.016652801 x = 20.016652801 Simplifying x = 20.016652801Subproblem 2
x + -10 = -10.016652801 Simplifying x + -10 = -10.016652801 Reorder the terms: -10 + x = -10.016652801 Solving -10 + x = -10.016652801 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 = -10.016652801 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.016652801 + 10 x = -10.016652801 + 10 Combine like terms: -10.016652801 + 10 = -0.016652801 x = -0.016652801 Simplifying x = -0.016652801Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.016652801, -0.016652801}
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