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Simplifying 3x(x + 20) = 8 Reorder the terms: 3x(20 + x) = 8 (20 * 3x + x * 3x) = 8 (60x + 3x2) = 8 Solving 60x + 3x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 60x + 3x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 60x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + 20x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 20x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 20x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 20x + x2 = 0 + 2.666666667 20x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 20x + x2 = 2.666666667 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 = 2.666666667 + 100 Reorder the terms: 100 + 20x + x2 = 2.666666667 + 100 Combine like terms: 2.666666667 + 100 = 102.666666667 100 + 20x + x2 = 102.666666667 Factor a perfect square on the left side: (x + 10)(x + 10) = 102.666666667 Calculate the square root of the right side: 10.132456102 Break this problem into two subproblems by setting (x + 10) equal to 10.132456102 and -10.132456102.Subproblem 1
x + 10 = 10.132456102 Simplifying x + 10 = 10.132456102 Reorder the terms: 10 + x = 10.132456102 Solving 10 + x = 10.132456102 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 = 10.132456102 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.132456102 + -10 x = 10.132456102 + -10 Combine like terms: 10.132456102 + -10 = 0.132456102 x = 0.132456102 Simplifying x = 0.132456102Subproblem 2
x + 10 = -10.132456102 Simplifying x + 10 = -10.132456102 Reorder the terms: 10 + x = -10.132456102 Solving 10 + x = -10.132456102 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 = -10.132456102 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.132456102 + -10 x = -10.132456102 + -10 Combine like terms: -10.132456102 + -10 = -20.132456102 x = -20.132456102 Simplifying x = -20.132456102Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.132456102, -20.132456102}
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