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Simplifying x2 + -400x + 7500 = 0 Reorder the terms: 7500 + -400x + x2 = 0 Solving 7500 + -400x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7500' to each side of the equation. 7500 + -400x + -7500 + x2 = 0 + -7500 Reorder the terms: 7500 + -7500 + -400x + x2 = 0 + -7500 Combine like terms: 7500 + -7500 = 0 0 + -400x + x2 = 0 + -7500 -400x + x2 = 0 + -7500 Combine like terms: 0 + -7500 = -7500 -400x + x2 = -7500 The x term is -400x. Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. -400x + 40000 + x2 = -7500 + 40000 Reorder the terms: 40000 + -400x + x2 = -7500 + 40000 Combine like terms: -7500 + 40000 = 32500 40000 + -400x + x2 = 32500 Factor a perfect square on the left side: (x + -200)(x + -200) = 32500 Calculate the square root of the right side: 180.277563773 Break this problem into two subproblems by setting (x + -200) equal to 180.277563773 and -180.277563773.Subproblem 1
x + -200 = 180.277563773 Simplifying x + -200 = 180.277563773 Reorder the terms: -200 + x = 180.277563773 Solving -200 + x = 180.277563773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = 180.277563773 + 200 Combine like terms: -200 + 200 = 0 0 + x = 180.277563773 + 200 x = 180.277563773 + 200 Combine like terms: 180.277563773 + 200 = 380.277563773 x = 380.277563773 Simplifying x = 380.277563773Subproblem 2
x + -200 = -180.277563773 Simplifying x + -200 = -180.277563773 Reorder the terms: -200 + x = -180.277563773 Solving -200 + x = -180.277563773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = -180.277563773 + 200 Combine like terms: -200 + 200 = 0 0 + x = -180.277563773 + 200 x = -180.277563773 + 200 Combine like terms: -180.277563773 + 200 = 19.722436227 x = 19.722436227 Simplifying x = 19.722436227Solution
The solution to the problem is based on the solutions from the subproblems. x = {380.277563773, 19.722436227}
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