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Simplifying x2 + -20x + -1 = 7 Reorder the terms: -1 + -20x + x2 = 7 Solving -1 + -20x + x2 = 7 Solving for variable 'x'. Reorder the terms: -1 + -7 + -20x + x2 = 7 + -7 Combine like terms: -1 + -7 = -8 -8 + -20x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -8 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -20x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -20x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -20x + x2 = 0 + 8 -20x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -20x + x2 = 8 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 = 8 + 100 Reorder the terms: 100 + -20x + x2 = 8 + 100 Combine like terms: 8 + 100 = 108 100 + -20x + x2 = 108 Factor a perfect square on the left side: (x + -10)(x + -10) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + -10) equal to 10.392304845 and -10.392304845.Subproblem 1
x + -10 = 10.392304845 Simplifying x + -10 = 10.392304845 Reorder the terms: -10 + x = 10.392304845 Solving -10 + x = 10.392304845 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 = 10.392304845 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.392304845 + 10 x = 10.392304845 + 10 Combine like terms: 10.392304845 + 10 = 20.392304845 x = 20.392304845 Simplifying x = 20.392304845Subproblem 2
x + -10 = -10.392304845 Simplifying x + -10 = -10.392304845 Reorder the terms: -10 + x = -10.392304845 Solving -10 + x = -10.392304845 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 = -10.392304845 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.392304845 + 10 x = -10.392304845 + 10 Combine like terms: -10.392304845 + 10 = -0.392304845 x = -0.392304845 Simplifying x = -0.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.392304845, -0.392304845}
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