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Simplifying x2 = 20x + 2 Reorder the terms: x2 = 2 + 20x Solving x2 = 2 + 20x Solving for variable 'x'. Reorder the terms: -2 + -20x + x2 = 2 + 20x + -2 + -20x Reorder the terms: -2 + -20x + x2 = 2 + -2 + 20x + -20x Combine like terms: 2 + -2 = 0 -2 + -20x + x2 = 0 + 20x + -20x -2 + -20x + x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -2 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -20x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -20x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -20x + x2 = 0 + 2 -20x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -20x + x2 = 2 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 2 + 100 Reorder the terms: 100 + -20x + x2 = 2 + 100 Combine like terms: 2 + 100 = 102 100 + -20x + x2 = 102 Factor a perfect square on the left side: (x + -10)(x + -10) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (x + -10) equal to 10.099504938 and -10.099504938.Subproblem 1
x + -10 = 10.099504938 Simplifying x + -10 = 10.099504938 Reorder the terms: -10 + x = 10.099504938 Solving -10 + x = 10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 10.099504938 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.099504938 + 10 x = 10.099504938 + 10 Combine like terms: 10.099504938 + 10 = 20.099504938 x = 20.099504938 Simplifying x = 20.099504938Subproblem 2
x + -10 = -10.099504938 Simplifying x + -10 = -10.099504938 Reorder the terms: -10 + x = -10.099504938 Solving -10 + x = -10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -10.099504938 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.099504938 + 10 x = -10.099504938 + 10 Combine like terms: -10.099504938 + 10 = -0.099504938 x = -0.099504938 Simplifying x = -0.099504938Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.099504938, -0.099504938}
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