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Simplifying x2 + -20x + -5 = 0 Reorder the terms: -5 + -20x + x2 = 0 Solving -5 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -20x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -20x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -20x + x2 = 0 + 5 -20x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -20x + x2 = 5 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 = 5 + 100 Reorder the terms: 100 + -20x + x2 = 5 + 100 Combine like terms: 5 + 100 = 105 100 + -20x + x2 = 105 Factor a perfect square on the left side: (x + -10)(x + -10) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + -10) equal to 10.246950766 and -10.246950766.Subproblem 1
x + -10 = 10.246950766 Simplifying x + -10 = 10.246950766 Reorder the terms: -10 + x = 10.246950766 Solving -10 + x = 10.246950766 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 = 10.246950766 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.246950766 + 10 x = 10.246950766 + 10 Combine like terms: 10.246950766 + 10 = 20.246950766 x = 20.246950766 Simplifying x = 20.246950766Subproblem 2
x + -10 = -10.246950766 Simplifying x + -10 = -10.246950766 Reorder the terms: -10 + x = -10.246950766 Solving -10 + x = -10.246950766 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 = -10.246950766 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.246950766 + 10 x = -10.246950766 + 10 Combine like terms: -10.246950766 + 10 = -0.246950766 x = -0.246950766 Simplifying x = -0.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.246950766, -0.246950766}
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