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Simplifying (75 + x)(x + 75) = 11250 Reorder the terms: (75 + x)(75 + x) = 11250 Multiply (75 + x) * (75 + x) (75(75 + x) + x(75 + x)) = 11250 ((75 * 75 + x * 75) + x(75 + x)) = 11250 ((5625 + 75x) + x(75 + x)) = 11250 (5625 + 75x + (75 * x + x * x)) = 11250 (5625 + 75x + (75x + x2)) = 11250 Combine like terms: 75x + 75x = 150x (5625 + 150x + x2) = 11250 Solving 5625 + 150x + x2 = 11250 Solving for variable 'x'. Reorder the terms: 5625 + -11250 + 150x + x2 = 11250 + -11250 Combine like terms: 5625 + -11250 = -5625 -5625 + 150x + x2 = 11250 + -11250 Combine like terms: 11250 + -11250 = 0 -5625 + 150x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5625' to each side of the equation. -5625 + 150x + 5625 + x2 = 0 + 5625 Reorder the terms: -5625 + 5625 + 150x + x2 = 0 + 5625 Combine like terms: -5625 + 5625 = 0 0 + 150x + x2 = 0 + 5625 150x + x2 = 0 + 5625 Combine like terms: 0 + 5625 = 5625 150x + x2 = 5625 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 = 5625 + 5625 Reorder the terms: 5625 + 150x + x2 = 5625 + 5625 Combine like terms: 5625 + 5625 = 11250 5625 + 150x + x2 = 11250 Factor a perfect square on the left side: (x + 75)(x + 75) = 11250 Calculate the square root of the right side: 106.066017178 Break this problem into two subproblems by setting (x + 75) equal to 106.066017178 and -106.066017178.Subproblem 1
x + 75 = 106.066017178 Simplifying x + 75 = 106.066017178 Reorder the terms: 75 + x = 106.066017178 Solving 75 + x = 106.066017178 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 = 106.066017178 + -75 Combine like terms: 75 + -75 = 0 0 + x = 106.066017178 + -75 x = 106.066017178 + -75 Combine like terms: 106.066017178 + -75 = 31.066017178 x = 31.066017178 Simplifying x = 31.066017178Subproblem 2
x + 75 = -106.066017178 Simplifying x + 75 = -106.066017178 Reorder the terms: 75 + x = -106.066017178 Solving 75 + x = -106.066017178 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 = -106.066017178 + -75 Combine like terms: 75 + -75 = 0 0 + x = -106.066017178 + -75 x = -106.066017178 + -75 Combine like terms: -106.066017178 + -75 = -181.066017178 x = -181.066017178 Simplifying x = -181.066017178Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.066017178, -181.066017178}
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