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Simplifying x2 + 20x + -8 = 0 Reorder the terms: -8 + 20x + x2 = 0 Solving -8 + 20x + x2 = 0 Solving for variable 'x'. 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 = 0.392304845 x = 0.392304845 Simplifying x = 0.392304845Subproblem 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 = -20.392304845 x = -20.392304845 Simplifying x = -20.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.392304845, -20.392304845}
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