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Simplifying x2 + -20x + 1 = 18 Reorder the terms: 1 + -20x + x2 = 18 Solving 1 + -20x + x2 = 18 Solving for variable 'x'. Reorder the terms: 1 + -18 + -20x + x2 = 18 + -18 Combine like terms: 1 + -18 = -17 -17 + -20x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -17 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -20x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -20x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -20x + x2 = 0 + 17 -20x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -20x + x2 = 17 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 = 17 + 100 Reorder the terms: 100 + -20x + x2 = 17 + 100 Combine like terms: 17 + 100 = 117 100 + -20x + x2 = 117 Factor a perfect square on the left side: (x + -10)(x + -10) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + -10) equal to 10.816653826 and -10.816653826.Subproblem 1
x + -10 = 10.816653826 Simplifying x + -10 = 10.816653826 Reorder the terms: -10 + x = 10.816653826 Solving -10 + x = 10.816653826 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 = 10.816653826 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.816653826 + 10 x = 10.816653826 + 10 Combine like terms: 10.816653826 + 10 = 20.816653826 x = 20.816653826 Simplifying x = 20.816653826Subproblem 2
x + -10 = -10.816653826 Simplifying x + -10 = -10.816653826 Reorder the terms: -10 + x = -10.816653826 Solving -10 + x = -10.816653826 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 = -10.816653826 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.816653826 + 10 x = -10.816653826 + 10 Combine like terms: -10.816653826 + 10 = -0.816653826 x = -0.816653826 Simplifying x = -0.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.816653826, -0.816653826}
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