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Simplifying (75 + x)(x + 75) = (75) * 2 Reorder the terms: (75 + x)(75 + x) = (75) * 2 Multiply (75 + x) * (75 + x) (75(75 + x) + x(75 + x)) = (75) * 2 ((75 * 75 + x * 75) + x(75 + x)) = (75) * 2 ((5625 + 75x) + x(75 + x)) = (75) * 2 (5625 + 75x + (75 * x + x * x)) = (75) * 2 (5625 + 75x + (75x + x2)) = (75) * 2 Combine like terms: 75x + 75x = 150x (5625 + 150x + x2) = (75) * 2 Multiply 75 * 2 5625 + 150x + x2 = 150 Solving 5625 + 150x + x2 = 150 Solving for variable 'x'. Reorder the terms: 5625 + -150 + 150x + x2 = 150 + -150 Combine like terms: 5625 + -150 = 5475 5475 + 150x + x2 = 150 + -150 Combine like terms: 150 + -150 = 0 5475 + 150x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5475' to each side of the equation. 5475 + 150x + -5475 + x2 = 0 + -5475 Reorder the terms: 5475 + -5475 + 150x + x2 = 0 + -5475 Combine like terms: 5475 + -5475 = 0 0 + 150x + x2 = 0 + -5475 150x + x2 = 0 + -5475 Combine like terms: 0 + -5475 = -5475 150x + x2 = -5475 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 = -5475 + 5625 Reorder the terms: 5625 + 150x + x2 = -5475 + 5625 Combine like terms: -5475 + 5625 = 150 5625 + 150x + x2 = 150 Factor a perfect square on the left side: (x + 75)(x + 75) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (x + 75) equal to 12.247448714 and -12.247448714.Subproblem 1
x + 75 = 12.247448714 Simplifying x + 75 = 12.247448714 Reorder the terms: 75 + x = 12.247448714 Solving 75 + x = 12.247448714 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 = 12.247448714 + -75 Combine like terms: 75 + -75 = 0 0 + x = 12.247448714 + -75 x = 12.247448714 + -75 Combine like terms: 12.247448714 + -75 = -62.752551286 x = -62.752551286 Simplifying x = -62.752551286Subproblem 2
x + 75 = -12.247448714 Simplifying x + 75 = -12.247448714 Reorder the terms: 75 + x = -12.247448714 Solving 75 + x = -12.247448714 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 = -12.247448714 + -75 Combine like terms: 75 + -75 = 0 0 + x = -12.247448714 + -75 x = -12.247448714 + -75 Combine like terms: -12.247448714 + -75 = -87.247448714 x = -87.247448714 Simplifying x = -87.247448714Solution
The solution to the problem is based on the solutions from the subproblems. x = {-62.752551286, -87.247448714}
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