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Simplifying 3x(x + 20) = 1 Reorder the terms: 3x(20 + x) = 1 (20 * 3x + x * 3x) = 1 (60x + 3x2) = 1 Solving 60x + 3x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 60x + 3x2 = 1 + -1 Combine like terms: 1 + -1 = 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 = 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 = 0.016652801 x = 0.016652801 Simplifying x = 0.016652801Subproblem 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 = -20.016652801 x = -20.016652801 Simplifying x = -20.016652801Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.016652801, -20.016652801}
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