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Simplifying x2 + -100x + 400 = 0 Reorder the terms: 400 + -100x + x2 = 0 Solving 400 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-400' to each side of the equation. 400 + -100x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -100x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -100x + x2 = 0 + -400 -100x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -100x + x2 = -400 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -400 + 2500 Reorder the terms: 2500 + -100x + x2 = -400 + 2500 Combine like terms: -400 + 2500 = 2100 2500 + -100x + x2 = 2100 Factor a perfect square on the left side: (x + -50)(x + -50) = 2100 Calculate the square root of the right side: 45.82575695 Break this problem into two subproblems by setting (x + -50) equal to 45.82575695 and -45.82575695.Subproblem 1
x + -50 = 45.82575695 Simplifying x + -50 = 45.82575695 Reorder the terms: -50 + x = 45.82575695 Solving -50 + x = 45.82575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 45.82575695 + 50 Combine like terms: -50 + 50 = 0 0 + x = 45.82575695 + 50 x = 45.82575695 + 50 Combine like terms: 45.82575695 + 50 = 95.82575695 x = 95.82575695 Simplifying x = 95.82575695Subproblem 2
x + -50 = -45.82575695 Simplifying x + -50 = -45.82575695 Reorder the terms: -50 + x = -45.82575695 Solving -50 + x = -45.82575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -45.82575695 + 50 Combine like terms: -50 + 50 = 0 0 + x = -45.82575695 + 50 x = -45.82575695 + 50 Combine like terms: -45.82575695 + 50 = 4.17424305 x = 4.17424305 Simplifying x = 4.17424305Solution
The solution to the problem is based on the solutions from the subproblems. x = {95.82575695, 4.17424305}
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