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Simplifying (x + 20)(x + 10) = 180 Reorder the terms: (20 + x)(x + 10) = 180 Reorder the terms: (20 + x)(10 + x) = 180 Multiply (20 + x) * (10 + x) (20(10 + x) + x(10 + x)) = 180 ((10 * 20 + x * 20) + x(10 + x)) = 180 ((200 + 20x) + x(10 + x)) = 180 (200 + 20x + (10 * x + x * x)) = 180 (200 + 20x + (10x + x2)) = 180 Combine like terms: 20x + 10x = 30x (200 + 30x + x2) = 180 Solving 200 + 30x + x2 = 180 Solving for variable 'x'. Reorder the terms: 200 + -180 + 30x + x2 = 180 + -180 Combine like terms: 200 + -180 = 20 20 + 30x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 20 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 30x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 30x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 30x + x2 = 0 + -20 30x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 30x + x2 = -20 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -20 + 225 Reorder the terms: 225 + 30x + x2 = -20 + 225 Combine like terms: -20 + 225 = 205 225 + 30x + x2 = 205 Factor a perfect square on the left side: (x + 15)(x + 15) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (x + 15) equal to 14.317821063 and -14.317821063.Subproblem 1
x + 15 = 14.317821063 Simplifying x + 15 = 14.317821063 Reorder the terms: 15 + x = 14.317821063 Solving 15 + x = 14.317821063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 14.317821063 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.317821063 + -15 x = 14.317821063 + -15 Combine like terms: 14.317821063 + -15 = -0.682178937 x = -0.682178937 Simplifying x = -0.682178937Subproblem 2
x + 15 = -14.317821063 Simplifying x + 15 = -14.317821063 Reorder the terms: 15 + x = -14.317821063 Solving 15 + x = -14.317821063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -14.317821063 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.317821063 + -15 x = -14.317821063 + -15 Combine like terms: -14.317821063 + -15 = -29.317821063 x = -29.317821063 Simplifying x = -29.317821063Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.682178937, -29.317821063}
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