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Simplifying 3x(x + 20) + 44 = 180 Reorder the terms: 3x(20 + x) + 44 = 180 (20 * 3x + x * 3x) + 44 = 180 (60x + 3x2) + 44 = 180 Reorder the terms: 44 + 60x + 3x2 = 180 Solving 44 + 60x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: 44 + -180 + 60x + 3x2 = 180 + -180 Combine like terms: 44 + -180 = -136 -136 + 60x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -136 + 60x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -45.33333333 + 20x + x2 = 0 Move the constant term to the right: Add '45.33333333' to each side of the equation. -45.33333333 + 20x + 45.33333333 + x2 = 0 + 45.33333333 Reorder the terms: -45.33333333 + 45.33333333 + 20x + x2 = 0 + 45.33333333 Combine like terms: -45.33333333 + 45.33333333 = 0.00000000 0.00000000 + 20x + x2 = 0 + 45.33333333 20x + x2 = 0 + 45.33333333 Combine like terms: 0 + 45.33333333 = 45.33333333 20x + x2 = 45.33333333 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 = 45.33333333 + 100 Reorder the terms: 100 + 20x + x2 = 45.33333333 + 100 Combine like terms: 45.33333333 + 100 = 145.33333333 100 + 20x + x2 = 145.33333333 Factor a perfect square on the left side: (x + 10)(x + 10) = 145.33333333 Calculate the square root of the right side: 12.055427547 Break this problem into two subproblems by setting (x + 10) equal to 12.055427547 and -12.055427547.Subproblem 1
x + 10 = 12.055427547 Simplifying x + 10 = 12.055427547 Reorder the terms: 10 + x = 12.055427547 Solving 10 + x = 12.055427547 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 = 12.055427547 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.055427547 + -10 x = 12.055427547 + -10 Combine like terms: 12.055427547 + -10 = 2.055427547 x = 2.055427547 Simplifying x = 2.055427547Subproblem 2
x + 10 = -12.055427547 Simplifying x + 10 = -12.055427547 Reorder the terms: 10 + x = -12.055427547 Solving 10 + x = -12.055427547 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 = -12.055427547 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.055427547 + -10 x = -12.055427547 + -10 Combine like terms: -12.055427547 + -10 = -22.055427547 x = -22.055427547 Simplifying x = -22.055427547Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.055427547, -22.055427547}
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