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Simplifying x2 = 200x + -100 Reorder the terms: x2 = -100 + 200x Solving x2 = -100 + 200x Solving for variable 'x'. Reorder the terms: 100 + -200x + x2 = -100 + 200x + 100 + -200x Reorder the terms: 100 + -200x + x2 = -100 + 100 + 200x + -200x Combine like terms: -100 + 100 = 0 100 + -200x + x2 = 0 + 200x + -200x 100 + -200x + x2 = 200x + -200x Combine like terms: 200x + -200x = 0 100 + -200x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -200x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -200x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -200x + x2 = 0 + -100 -200x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -200x + x2 = -100 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 = -100 + 10000 Reorder the terms: 10000 + -200x + x2 = -100 + 10000 Combine like terms: -100 + 10000 = 9900 10000 + -200x + x2 = 9900 Factor a perfect square on the left side: (x + -100)(x + -100) = 9900 Calculate the square root of the right side: 99.498743711 Break this problem into two subproblems by setting (x + -100) equal to 99.498743711 and -99.498743711.Subproblem 1
x + -100 = 99.498743711 Simplifying x + -100 = 99.498743711 Reorder the terms: -100 + x = 99.498743711 Solving -100 + x = 99.498743711 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 = 99.498743711 + 100 Combine like terms: -100 + 100 = 0 0 + x = 99.498743711 + 100 x = 99.498743711 + 100 Combine like terms: 99.498743711 + 100 = 199.498743711 x = 199.498743711 Simplifying x = 199.498743711Subproblem 2
x + -100 = -99.498743711 Simplifying x + -100 = -99.498743711 Reorder the terms: -100 + x = -99.498743711 Solving -100 + x = -99.498743711 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 = -99.498743711 + 100 Combine like terms: -100 + 100 = 0 0 + x = -99.498743711 + 100 x = -99.498743711 + 100 Combine like terms: -99.498743711 + 100 = 0.501256289 x = 0.501256289 Simplifying x = 0.501256289Solution
The solution to the problem is based on the solutions from the subproblems. x = {199.498743711, 0.501256289}
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