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Simplifying x2 + -75x + 1150 = 0 Reorder the terms: 1150 + -75x + x2 = 0 Solving 1150 + -75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1150' to each side of the equation. 1150 + -75x + -1150 + x2 = 0 + -1150 Reorder the terms: 1150 + -1150 + -75x + x2 = 0 + -1150 Combine like terms: 1150 + -1150 = 0 0 + -75x + x2 = 0 + -1150 -75x + x2 = 0 + -1150 Combine like terms: 0 + -1150 = -1150 -75x + x2 = -1150 The x term is -75x. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75x + 1406.25 + x2 = -1150 + 1406.25 Reorder the terms: 1406.25 + -75x + x2 = -1150 + 1406.25 Combine like terms: -1150 + 1406.25 = 256.25 1406.25 + -75x + x2 = 256.25 Factor a perfect square on the left side: (x + -37.5)(x + -37.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (x + -37.5) equal to 16.007810594 and -16.007810594.Subproblem 1
x + -37.5 = 16.007810594 Simplifying x + -37.5 = 16.007810594 Reorder the terms: -37.5 + x = 16.007810594 Solving -37.5 + x = 16.007810594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 16.007810594 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 16.007810594 + 37.5 x = 16.007810594 + 37.5 Combine like terms: 16.007810594 + 37.5 = 53.507810594 x = 53.507810594 Simplifying x = 53.507810594Subproblem 2
x + -37.5 = -16.007810594 Simplifying x + -37.5 = -16.007810594 Reorder the terms: -37.5 + x = -16.007810594 Solving -37.5 + x = -16.007810594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = -16.007810594 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -16.007810594 + 37.5 x = -16.007810594 + 37.5 Combine like terms: -16.007810594 + 37.5 = 21.492189406 x = 21.492189406 Simplifying x = 21.492189406Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.507810594, 21.492189406}
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