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Simplifying x2 + 128x + 375 = 750 Reorder the terms: 375 + 128x + x2 = 750 Solving 375 + 128x + x2 = 750 Solving for variable 'x'. Reorder the terms: 375 + -750 + 128x + x2 = 750 + -750 Combine like terms: 375 + -750 = -375 -375 + 128x + x2 = 750 + -750 Combine like terms: 750 + -750 = 0 -375 + 128x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '375' to each side of the equation. -375 + 128x + 375 + x2 = 0 + 375 Reorder the terms: -375 + 375 + 128x + x2 = 0 + 375 Combine like terms: -375 + 375 = 0 0 + 128x + x2 = 0 + 375 128x + x2 = 0 + 375 Combine like terms: 0 + 375 = 375 128x + x2 = 375 The x term is 128x. Take half its coefficient (64). Square it (4096) and add it to both sides. Add '4096' to each side of the equation. 128x + 4096 + x2 = 375 + 4096 Reorder the terms: 4096 + 128x + x2 = 375 + 4096 Combine like terms: 375 + 4096 = 4471 4096 + 128x + x2 = 4471 Factor a perfect square on the left side: (x + 64)(x + 64) = 4471 Calculate the square root of the right side: 66.865536714 Break this problem into two subproblems by setting (x + 64) equal to 66.865536714 and -66.865536714.Subproblem 1
x + 64 = 66.865536714 Simplifying x + 64 = 66.865536714 Reorder the terms: 64 + x = 66.865536714 Solving 64 + x = 66.865536714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + x = 66.865536714 + -64 Combine like terms: 64 + -64 = 0 0 + x = 66.865536714 + -64 x = 66.865536714 + -64 Combine like terms: 66.865536714 + -64 = 2.865536714 x = 2.865536714 Simplifying x = 2.865536714Subproblem 2
x + 64 = -66.865536714 Simplifying x + 64 = -66.865536714 Reorder the terms: 64 + x = -66.865536714 Solving 64 + x = -66.865536714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + x = -66.865536714 + -64 Combine like terms: 64 + -64 = 0 0 + x = -66.865536714 + -64 x = -66.865536714 + -64 Combine like terms: -66.865536714 + -64 = -130.865536714 x = -130.865536714 Simplifying x = -130.865536714Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.865536714, -130.865536714}
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