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Simplifying x2 + -200x + 400 = 0 Reorder the terms: 400 + -200x + x2 = 0 Solving 400 + -200x + 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 + -200x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -200x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -200x + x2 = 0 + -400 -200x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -200x + x2 = -400 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -400 + 10000 Reorder the terms: 10000 + -200x + x2 = -400 + 10000 Combine like terms: -400 + 10000 = 9600 10000 + -200x + x2 = 9600 Factor a perfect square on the left side: (x + -100)(x + -100) = 9600 Calculate the square root of the right side: 97.979589711 Break this problem into two subproblems by setting (x + -100) equal to 97.979589711 and -97.979589711.Subproblem 1
x + -100 = 97.979589711 Simplifying x + -100 = 97.979589711 Reorder the terms: -100 + x = 97.979589711 Solving -100 + x = 97.979589711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 97.979589711 + 100 Combine like terms: -100 + 100 = 0 0 + x = 97.979589711 + 100 x = 97.979589711 + 100 Combine like terms: 97.979589711 + 100 = 197.979589711 x = 197.979589711 Simplifying x = 197.979589711Subproblem 2
x + -100 = -97.979589711 Simplifying x + -100 = -97.979589711 Reorder the terms: -100 + x = -97.979589711 Solving -100 + x = -97.979589711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -97.979589711 + 100 Combine like terms: -100 + 100 = 0 0 + x = -97.979589711 + 100 x = -97.979589711 + 100 Combine like terms: -97.979589711 + 100 = 2.020410289 x = 2.020410289 Simplifying x = 2.020410289Solution
The solution to the problem is based on the solutions from the subproblems. x = {197.979589711, 2.020410289}
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