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Simplifying x2 + -20x + -99 = 0 Reorder the terms: -99 + -20x + x2 = 0 Solving -99 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -20x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -20x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -20x + x2 = 0 + 99 -20x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -20x + x2 = 99 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 = 99 + 100 Reorder the terms: 100 + -20x + x2 = 99 + 100 Combine like terms: 99 + 100 = 199 100 + -20x + x2 = 199 Factor a perfect square on the left side: (x + -10)(x + -10) = 199 Calculate the square root of the right side: 14.10673598 Break this problem into two subproblems by setting (x + -10) equal to 14.10673598 and -14.10673598.Subproblem 1
x + -10 = 14.10673598 Simplifying x + -10 = 14.10673598 Reorder the terms: -10 + x = 14.10673598 Solving -10 + x = 14.10673598 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 = 14.10673598 + 10 Combine like terms: -10 + 10 = 0 0 + x = 14.10673598 + 10 x = 14.10673598 + 10 Combine like terms: 14.10673598 + 10 = 24.10673598 x = 24.10673598 Simplifying x = 24.10673598Subproblem 2
x + -10 = -14.10673598 Simplifying x + -10 = -14.10673598 Reorder the terms: -10 + x = -14.10673598 Solving -10 + x = -14.10673598 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 = -14.10673598 + 10 Combine like terms: -10 + 10 = 0 0 + x = -14.10673598 + 10 x = -14.10673598 + 10 Combine like terms: -14.10673598 + 10 = -4.10673598 x = -4.10673598 Simplifying x = -4.10673598Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.10673598, -4.10673598}
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