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Simplifying x(x + 40) = 180 Reorder the terms: x(40 + x) = 180 (40 * x + x * x) = 180 (40x + x2) = 180 Solving 40x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 40x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 40x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 40x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 40x + x2 = 0 + 180 40x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 40x + x2 = 180 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 180 + 400 Reorder the terms: 400 + 40x + x2 = 180 + 400 Combine like terms: 180 + 400 = 580 400 + 40x + x2 = 580 Factor a perfect square on the left side: (x + 20)(x + 20) = 580 Calculate the square root of the right side: 24.083189158 Break this problem into two subproblems by setting (x + 20) equal to 24.083189158 and -24.083189158.Subproblem 1
x + 20 = 24.083189158 Simplifying x + 20 = 24.083189158 Reorder the terms: 20 + x = 24.083189158 Solving 20 + x = 24.083189158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 24.083189158 + -20 Combine like terms: 20 + -20 = 0 0 + x = 24.083189158 + -20 x = 24.083189158 + -20 Combine like terms: 24.083189158 + -20 = 4.083189158 x = 4.083189158 Simplifying x = 4.083189158Subproblem 2
x + 20 = -24.083189158 Simplifying x + 20 = -24.083189158 Reorder the terms: 20 + x = -24.083189158 Solving 20 + x = -24.083189158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -24.083189158 + -20 Combine like terms: 20 + -20 = 0 0 + x = -24.083189158 + -20 x = -24.083189158 + -20 Combine like terms: -24.083189158 + -20 = -44.083189158 x = -44.083189158 Simplifying x = -44.083189158Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.083189158, -44.083189158}
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