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Simplifying x(115 + x) = 570 (115 * x + x * x) = 570 (115x + x2) = 570 Solving 115x + x2 = 570 Solving for variable 'x'. Reorder the terms: -570 + 115x + x2 = 570 + -570 Combine like terms: 570 + -570 = 0 -570 + 115x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '570' to each side of the equation. -570 + 115x + 570 + x2 = 0 + 570 Reorder the terms: -570 + 570 + 115x + x2 = 0 + 570 Combine like terms: -570 + 570 = 0 0 + 115x + x2 = 0 + 570 115x + x2 = 0 + 570 Combine like terms: 0 + 570 = 570 115x + x2 = 570 The x term is 115x. Take half its coefficient (57.5). Square it (3306.25) and add it to both sides. Add '3306.25' to each side of the equation. 115x + 3306.25 + x2 = 570 + 3306.25 Reorder the terms: 3306.25 + 115x + x2 = 570 + 3306.25 Combine like terms: 570 + 3306.25 = 3876.25 3306.25 + 115x + x2 = 3876.25 Factor a perfect square on the left side: (x + 57.5)(x + 57.5) = 3876.25 Calculate the square root of the right side: 62.259537422 Break this problem into two subproblems by setting (x + 57.5) equal to 62.259537422 and -62.259537422.Subproblem 1
x + 57.5 = 62.259537422 Simplifying x + 57.5 = 62.259537422 Reorder the terms: 57.5 + x = 62.259537422 Solving 57.5 + x = 62.259537422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-57.5' to each side of the equation. 57.5 + -57.5 + x = 62.259537422 + -57.5 Combine like terms: 57.5 + -57.5 = 0.0 0.0 + x = 62.259537422 + -57.5 x = 62.259537422 + -57.5 Combine like terms: 62.259537422 + -57.5 = 4.759537422 x = 4.759537422 Simplifying x = 4.759537422Subproblem 2
x + 57.5 = -62.259537422 Simplifying x + 57.5 = -62.259537422 Reorder the terms: 57.5 + x = -62.259537422 Solving 57.5 + x = -62.259537422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-57.5' to each side of the equation. 57.5 + -57.5 + x = -62.259537422 + -57.5 Combine like terms: 57.5 + -57.5 = 0.0 0.0 + x = -62.259537422 + -57.5 x = -62.259537422 + -57.5 Combine like terms: -62.259537422 + -57.5 = -119.759537422 x = -119.759537422 Simplifying x = -119.759537422Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.759537422, -119.759537422}
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