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Simplifying (x + 10)(x + 20) = 180x Reorder the terms: (10 + x)(x + 20) = 180x Reorder the terms: (10 + x)(20 + x) = 180x Multiply (10 + x) * (20 + x) (10(20 + x) + x(20 + x)) = 180x ((20 * 10 + x * 10) + x(20 + x)) = 180x ((200 + 10x) + x(20 + x)) = 180x (200 + 10x + (20 * x + x * x)) = 180x (200 + 10x + (20x + x2)) = 180x Combine like terms: 10x + 20x = 30x (200 + 30x + x2) = 180x Solving 200 + 30x + x2 = 180x Solving for variable 'x'. Reorder the terms: 200 + 30x + -180x + x2 = 180x + -180x Combine like terms: 30x + -180x = -150x 200 + -150x + x2 = 180x + -180x Combine like terms: 180x + -180x = 0 200 + -150x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -150x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -150x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -150x + x2 = 0 + -200 -150x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -150x + x2 = -200 The x term is -150x. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150x + 5625 + x2 = -200 + 5625 Reorder the terms: 5625 + -150x + x2 = -200 + 5625 Combine like terms: -200 + 5625 = 5425 5625 + -150x + x2 = 5425 Factor a perfect square on the left side: (x + -75)(x + -75) = 5425 Calculate the square root of the right side: 73.654599313 Break this problem into two subproblems by setting (x + -75) equal to 73.654599313 and -73.654599313.Subproblem 1
x + -75 = 73.654599313 Simplifying x + -75 = 73.654599313 Reorder the terms: -75 + x = 73.654599313 Solving -75 + x = 73.654599313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 73.654599313 + 75 Combine like terms: -75 + 75 = 0 0 + x = 73.654599313 + 75 x = 73.654599313 + 75 Combine like terms: 73.654599313 + 75 = 148.654599313 x = 148.654599313 Simplifying x = 148.654599313Subproblem 2
x + -75 = -73.654599313 Simplifying x + -75 = -73.654599313 Reorder the terms: -75 + x = -73.654599313 Solving -75 + x = -73.654599313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -73.654599313 + 75 Combine like terms: -75 + 75 = 0 0 + x = -73.654599313 + 75 x = -73.654599313 + 75 Combine like terms: -73.654599313 + 75 = 1.345400687 x = 1.345400687 Simplifying x = 1.345400687Solution
The solution to the problem is based on the solutions from the subproblems. x = {148.654599313, 1.345400687}
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