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Simplifying 3x(x + 20) = 44 Reorder the terms: 3x(20 + x) = 44 (20 * 3x + x * 3x) = 44 (60x + 3x2) = 44 Solving 60x + 3x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + 60x + 3x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 60x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14.66666667 + 20x + x2 = 0 Move the constant term to the right: Add '14.66666667' to each side of the equation. -14.66666667 + 20x + 14.66666667 + x2 = 0 + 14.66666667 Reorder the terms: -14.66666667 + 14.66666667 + 20x + x2 = 0 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + 20x + x2 = 0 + 14.66666667 20x + x2 = 0 + 14.66666667 Combine like terms: 0 + 14.66666667 = 14.66666667 20x + x2 = 14.66666667 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 = 14.66666667 + 100 Reorder the terms: 100 + 20x + x2 = 14.66666667 + 100 Combine like terms: 14.66666667 + 100 = 114.66666667 100 + 20x + x2 = 114.66666667 Factor a perfect square on the left side: (x + 10)(x + 10) = 114.66666667 Calculate the square root of the right side: 10.70825227 Break this problem into two subproblems by setting (x + 10) equal to 10.70825227 and -10.70825227.Subproblem 1
x + 10 = 10.70825227 Simplifying x + 10 = 10.70825227 Reorder the terms: 10 + x = 10.70825227 Solving 10 + x = 10.70825227 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 = 10.70825227 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.70825227 + -10 x = 10.70825227 + -10 Combine like terms: 10.70825227 + -10 = 0.70825227 x = 0.70825227 Simplifying x = 0.70825227Subproblem 2
x + 10 = -10.70825227 Simplifying x + 10 = -10.70825227 Reorder the terms: 10 + x = -10.70825227 Solving 10 + x = -10.70825227 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 = -10.70825227 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.70825227 + -10 x = -10.70825227 + -10 Combine like terms: -10.70825227 + -10 = -20.70825227 x = -20.70825227 Simplifying x = -20.70825227Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.70825227, -20.70825227}
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