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Simplifying x + 3x(x + 40) = 180 Reorder the terms: x + 3x(40 + x) = 180 x + (40 * 3x + x * 3x) = 180 x + (120x + 3x2) = 180 Combine like terms: x + 120x = 121x 121x + 3x2 = 180 Solving 121x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 121x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 121x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -60 + 40.33333333x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 40.33333333x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 40.33333333x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 40.33333333x + x2 = 0 + 60 40.33333333x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 40.33333333x + x2 = 60 The x term is 40.33333333x. Take half its coefficient (20.16666667). Square it (406.6944446) and add it to both sides. Add '406.6944446' to each side of the equation. 40.33333333x + 406.6944446 + x2 = 60 + 406.6944446 Reorder the terms: 406.6944446 + 40.33333333x + x2 = 60 + 406.6944446 Combine like terms: 60 + 406.6944446 = 466.6944446 406.6944446 + 40.33333333x + x2 = 466.6944446 Factor a perfect square on the left side: (x + 20.16666667)(x + 20.16666667) = 466.6944446 Calculate the square root of the right side: 21.603111919 Break this problem into two subproblems by setting (x + 20.16666667) equal to 21.603111919 and -21.603111919.Subproblem 1
x + 20.16666667 = 21.603111919 Simplifying x + 20.16666667 = 21.603111919 Reorder the terms: 20.16666667 + x = 21.603111919 Solving 20.16666667 + x = 21.603111919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.16666667' to each side of the equation. 20.16666667 + -20.16666667 + x = 21.603111919 + -20.16666667 Combine like terms: 20.16666667 + -20.16666667 = 0.00000000 0.00000000 + x = 21.603111919 + -20.16666667 x = 21.603111919 + -20.16666667 Combine like terms: 21.603111919 + -20.16666667 = 1.436445249 x = 1.436445249 Simplifying x = 1.436445249Subproblem 2
x + 20.16666667 = -21.603111919 Simplifying x + 20.16666667 = -21.603111919 Reorder the terms: 20.16666667 + x = -21.603111919 Solving 20.16666667 + x = -21.603111919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.16666667' to each side of the equation. 20.16666667 + -20.16666667 + x = -21.603111919 + -20.16666667 Combine like terms: 20.16666667 + -20.16666667 = 0.00000000 0.00000000 + x = -21.603111919 + -20.16666667 x = -21.603111919 + -20.16666667 Combine like terms: -21.603111919 + -20.16666667 = -41.769778589 x = -41.769778589 Simplifying x = -41.769778589Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.436445249, -41.769778589}
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